# concise mathematics class 7 lines and angles

MORE ABOUT ANGLES : (A) Angles about a point: If a number of angles are formed about a point, their sum is always 360°. Answer, Use the adjacent figure, to find angle x and its supplement. (ix) ∠5 and ∠7 are adjacent angles. Mark a point A in PQ so that AP = 2 cm. (ii) 37° 28′ and 52° 33′ Contact us on below numbers. ∴l3 and l5 are not parallel But ∠1 = 80° (alternate angles) ⇒ 80° = 80° Which is true ∴ l2 and l4 are parallel (vi) Lines are parallel If alternate angles are equal ⇒ 50° = 40° Wliich is not ture lines are not parallel. Acute angle : measures less than 90° 2. If 3x + 18° and 2x + 25° are supplementary, find the value of x. (vii) ∠1 and ∠5 (c) a lineAB (vi) ∠11 and ∠8 Lines and angles class 7 provides knowledge about basic geometry. (v) Bisect arc LM at N. (vi) Join PN and produce it to Q. Selina Solutions Concise Maths Class 7 Chapter 14 Lines and Angles (Including Construction of Angles) are designed by highly knowledgeable faculty at BYJU’S, keeping in mind the understanding capacity of students. Find each angle shown in the diagram. COMPLEMENTARY AND SUPPLEMENTARY ANGLES 1. Academic Partner. At P, draw perpendicular to AB. Then ∠ABC = 180°. (i) The adjoining figure shows a line AB which can be extended upto infinitey on both the sides of it. (vii) 37.5° Here, we are going to discuss the various types of angle, its measure, parallel lines angle formed using lines, etc. (iii) The adjoining figure shows a line-segment AB with fixed ends A and B. Important: In the adjoining figure, rays OX and OY meet a O to form ∠XOY (i.e. Solution: In the figure (i), a = b (corresponding angles) b = c (vertically opposite angles) a = c (alternate angles) ∴ a = b = c (ii) In the figure (ii), x =y (vertically opposite angles) y=l (alternate angles) x = I (corresponding angles) 1 = n (vertically opposite angles) n = r (corresponding angles) ∴ x = y = l = n = r Again m = k (vertically opposite angles) k = q (corresponding angles) ∴ m = k = q, Question 4. (ii) With centre B and some suitable radius, draw an arc meeting BC at P. (iii) With centre P and with same radius, cut arcs PQ and then QR. ∠1 = ∠5;∠2 = ∠6;∠3 = ∠7 and ∠4 = ∠8 (iii) Co-interior or allied angles are supplementary : i. e. ∠3 + ∠5 = 180° and ∠4 +∠6 = 180°. The two line segments, forming an angle, are called the arms of the angle whereas their common end-point is called the vertex of the angle. Find k in each of the given figures. Here you get easy solutions of ICSE class 7 Math Book Chapter 14. Corpus ID: 199674122. (iii) (x+ 16)°and(74-x)° Mathematics / Lines and Angles. (a) collinear points? (i) ∠1 and ∠4 (ii) ∠4 and ∠7 (iii) ∠10 and ∠12 (iv) ∠7 and ∠13 (v) ∠6 and ∠8 (vi) ∠11 and ∠8 (vii) ∠7 and ∠9 (viii) ∠4 and ∠5 (ix) ∠4 and ∠6 (x) ∠6 and ∠7 (xi) ∠2 and ∠13 Solution: (i) ∠1 and ∠4 are vertically opposite angles. Answer, Are the following pairs of angles supplementary? (ii) With centre B and some suitable radius draw an arc meeting BC at P. (iii) With centre P and same radius cut off arcs PQ, QR and then RS. Then ∠ABC = 67$$\frac { 1 }{ 2 }$$ ° or 67.5°. Solution: If ∠AOB and ∠AOC are adjacent angle if they have OA their common arm. (iii) ∠10 and ∠12 are vertically opposite angles. Education Franchise × Contact Us. Solution: Question 18. Mark a point P in AB such that PB = 3.6 cm. (ii) With centre B and a suitable radius draw an arc meeting BC at P. (iii) With centre P and with same radius cut off the arc at Q. Answer, Construct an angle of 75° and then bisect it. e.g., 30″ and 150° are supplementary angles because 30° + 150° = 180°. The symbol for degree is °. (iv) ∠2 and ∠7 Solution: Question 9. (i) ∠3 and ∠6 (ii) ∠2 and ∠4 (iii) ∠3 and ∠7 (iv) ∠2 and ∠7 (v) ∠4 and∠6 (vi) ∠1 and ∠8 (vii) ∠1 and ∠5 (viii) ∠1 and ∠4 (ix) ∠5 and ∠7 Solution: (i) ∠3 and ∠6 are interior alternate angles. Two angles are called complementary angles, if their sum is one’right angle i.e. Solution: Question 21. Mark a point P in AB so that AP = 5 cm. In the adjoining figure, if b° = a° + c°, find b. Question 2. (i) 10° and 80° (ii) 37° 28′ and 52° 33′ (iii) (x+ 16)°and(74-x)° (iv) 54° and $$\frac { 2 }{ 5 }$$ of a right angle. Solution: Question 17. When two parallel lines AB and CD are cut by a transversal PQ : (i) Interior and exterior alternate angles are equal: i.e. (ii) Mark a point P in AB such that AP = 5 cm. Answer, In the given figure, lines PQ, MN and RS intersect at O. Answer, Find k in each of the given figures. Solution: SQR is a straight line ∴∠SQT + ∠TQP + ∠PQR = 180° ⇒ x + 70° + 20° – x + ∠PQR = 180° ⇒ 90″ + ∠PQR = 180° ⇒ ∠PQR = 180°-90° = 90° Hence ∠PQR = 90°. Angle: Complementary ... ACCESS Math: Online Textbook Help. Solution: Steps of Construction : (i) Draw a line segment BC. Are the following pairs of angles supplementary? (ix) ∠4 and ∠6 are allied or co-interior angles. 7. This will clear students doubts about any question and improve application skills while preparing for board exams. Which pair of the dotted line, segments, in the following figures, are parallel. e.g., 20″ and 70″ are complementary angles, because 20° + 70° = 90°. Transversal : It is a straight line which cuts two or more given straight lines. 2. Answer, In the given figure, if x = 2y, find x and y (viii) 67.5° Steps of Construction : (i) Draw a line segment BC. 1. Shaalaa has a total of 124 questions with solutions for this chapter in Class 7 Maths. (v) Bisect arc QR at S and join BS. Two pairs of interior alternate angles : Angles marked 1 and 2 form one pair of interior alternate angles, while angles marked 3 and 4 form another pair of interior alternate angles. (iii) ∠3 and ∠7 are corresponding angles. (ii) True (iii) True (iv) True (v) (a) 2 (b) 1 (c) 0 (vi) AB (vii) Infinite (viii) (a) 1 (b) 3 (ix) False : 40° is the complement of 50° as 40° + 50° = 90° (x) False : 45° is the supplement of 135° not 45°. PARALLEL LINES : Two straight lines are said to be parallel, if , they do not meet anywhere; no matter how long are they produced in any direction. (iv) 180° (iii) 75° Steps of Construction : (i) Draw a line segment BC. For each angle given below, write the name of the vertex, the names of the arms and the name of the angle. I have done 22 videos on Lines and Angles chapter from CBSE / NCERT book Clearly, 30″ is the supplement of 150° and vice-versa. ∠a) and reflex ∠XOY (i. e. ∠b). In the given figure, B AC is a straight line. If x : y = 1 : 2 and z = 90°, find ∠ROM and ∠POR. Give, in each case, reason for your answer. Jul 26, 2019 - Contents1 Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles (Including Construction of angles)1.1 Lines and Angles Exercise 14A – Selina Concise Mathematics Class 7 ICSE Solutions1.2 Lines and Angles Exercise 14B – Selina Concise Mathematics Class 7 ICSE Solutions1.3 Lines and Angles Exercise 14C – Selina Concise Mathematics Class 7 … (ii) In the figure, OC is their common arm ∴∠AOB and ∠AOC also not adjacent angles. (v) ∠4 and∠6 Measure each 1 angle so obtained and check whether the angles obtained on bisecting ∠ABC are equal or not. Answer, In the given figure, find ∠AOB and ∠BOC. Find : (i) x (ii) ∠AOB (iii) ∠BOC Solution: Question 4. POINT : A point: is a mark of position; which has no length, no breadth and no thickness. Answer, Draw a line segment AB = 5.8 cm. Draw a line segment of length 6 .4 cm. Write the complement of: Solution: Question 11. Question 6. Then ∠ABC = 75°. (iii) 75° Apr 25, 2019 - Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles (Including Construction of angles) Selina Publishers Concise Maths Class 7 ICSE Solutions Chapter 14 Lines and Angles (Including Construction of angles) ICSE SolutionsSelina ICSE SolutionsML Aggarwal Solutions APlusTopper.com provides step by step solutions for Selina Concise ICSE Solutions for Class 7 … In each case, given below, draw a line through point P and parallel to AB : Solution: Steps of construction : (i) From P. draw a line segment meeting AB at (ii) With centre Q and some suitable radius draw an arc CD. (ix) Is 40° the complement of 60°? Give reason: Solution: (i) In figure (i), If lines are parallel, then 120°+ 50° =180° But there are co-interior angles ⇒170° = 180°. Answer, If two supplementary’ angles are in the ratio 2 : 7, find them. Question 3. Find the angle which is equal to its complement. … Answer, In the given figure, find the measure of the unknown angles : (iv) Taking P and Q as curves, draw two arcs intersecting each other at D nnd join BD. Which pair of the dotted line, segments, in the following figures, are parallel. Answer. (ii)15° Solution: Steps of Construction : (i) Draw a line segment AB = 5.8 cm. 4. (ii) ∠2 and ∠4 are adjacent angles. Contact. (iii) With centre Q and R, draw two arcs intersecting each other at S. (iv) Join SB. (iii) With centre P and same radius draw another arc meeting PQ at E. (iv) With centre E and radius equal to CD, cut this arc at F (v) Join PF and produce it to both sides to L and M. Then line LM is parallel to given line AB. (iv) Now bisect arc QR at S and again bisect arc QS at T. (v) Bisect arc PT at K. (vi) Join BK and produce it to A. We provide step by step Solutions of Exercise / lesson-14 Lines and Angles (Including Construction of angles) for ICSE Class-7 Concise Selina Mathematics. Answer, Find each angle shown in the diagram. Then ∠ABC = 165°. At point A, construct angle QAR = 60°. Solution: Steps of Construction : (i) Draw a line segment AB = 8 cm. The PDF of solutions prepare students to solve problems without any difficulty. TYPES OF ANGLES : 1. Solution: Question 15. Selina Concise Mathematics class 7 ICSE Solutions - Lines ... ... Maths (iii) ∠3 and ∠7 (v) ∠6 and ∠8 May 26, 2018 - Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles (Including Construction of angles) Selina Publishers Concise Maths Class 7 ICSE Solutions Chapter 14 Lines and Angles (Including Construction of angles) ICSE SolutionsSelina ICSE SolutionsML Aggarwal Solutions APlusTopper.com provides step by… (iv) An infinite number of straight lines can be drawn through a given point. State Books Bihar UP Andhra Pradesh Chhattisgarh Gujarat Karnataka Kerala Madhya Pradesh Maharashtra Punjab Rajasthan Tamilnadu Telangana ICSE NIOS Odisha Board. In the adjoining figure, two straight lines AB and CD intersect each other at point 0. (iv) Join SB. Answer, Find x in the following cases : Lines and Angles. It is clear from the figure, that a line-segment is a part of a ray as well as of a line. In questions 1 and 2, given below, identify the given pairs of angles as corresponding angles, interior alternate angles, exterior alternate angles, adjacent angles, vertically opposite angles or allied angles : (i) ∠3 and ∠6 (vi) Out of  ,  ,  and  , which one has a fixed length? (i) Find x, if y = 45° and z = 90°. Question 6. In the given figure, find ∠PQR. Answer, Find x. y and p is the given figures Right angle: measures 90° 3. In the given figure, find ∠AOB and ∠BOC. Find the unknown angles. (ii) With centre B and some suitable radius, draw an arc meeting BC at P. (iii) With centre P and with same radius, cut arcs PQ and QR. (iii) ∠10 and ∠12 Question 3. (iii) x° Yes, both angles are equal in measure. (i) 10° and 80° It, in general, is represented by a capital letter as shown alongside. (ii) With centre B and some suitable radius, draw an arc meeting BC at P. (iii) With centre P and same radius cut off arcs PQ and QR. The corners made by the intersection of two lines or line segments are called Angles. (iii) With centre A and some suitable radius draw an arc meeting AQ at C. (iv) With centre C and with same radius, cut arc CB. Answer, Draw ∠ABC = 120°. There are different types of angles based on the position of the arms. (iv) ∠7 and ∠13 In the given figure. Find the angle. Mark a point A in PQ so that AP = 2 cm. Answer. Bisect the angle using ruler and compasses only. In which of the following figures, are ∠AOB and ∠AOC adjacent angles? Draw ∠ABC = 120°. Find : (i) the value of x. Question 5. (C) Vertically opposite angles : When two straight lines intersect each other four angles are formed. (iii) A line segment is the shortest distance between any two given points. NCERT Books & Solutions … Get Selina concise solutions for class 7 maths for all chapters. (vii)  of a right angle In the given figure, AB is perpendicular to BC at B. (v) 165° Therefore, in order to prove that the given lines are parallel, show either alternate angles are equal or, corresponding angles are equal or, the co-interior angles are supplementary. Clearly, 20″ is the complement of 70° and 70° is the complement of 20°. Solution: Question 25. (i) 100° Four pairs of corresponding angles : Angles marked 3 and 6; 1 and 5; 8 and 2; 7 and 4 form the four pairs of corresponding angles. (iv) ∠7 and ∠13 are corresponding angles. Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles @inproceedings{Ram2019SelinaCM, title={Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles}, author={Ram}, year={2019} } Write the supplement of: (i) 100° (ii) 0° (iii) x° (iv) (x + 35)° (v) (90 +a + b)° f (vi) (110 – x – 2y)° (vii) $$\frac { 1 }{ 5 }$$ of a right angle (viii) 80° 49′ 25″ Solution: Question 12. When 2 lines meet at a point, they form an angle at that point. 10. Draw a line segment PQ = 6 cm. 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