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Question 1.Lines AC and BD intersect at point P. m∠APD = 47° Find the measures of ∠APB, ∠BPC, ∠CPD. Solution:∠APD and ∠APB are angles in a linear pair.∴m∠APD + m∠APB = 180°∴47 + m∠APB = 180∴47 + m∠APB – 47 = 180 – 47 ….(Subtracting 47 from both sides)∴m∠APB = 133°m∠CPD = m∠APB = 133° … Read more

Question 1.Draw the pairs of angles as described below. If that is not possible, say why.i. Complementary angles that are not adjacent.ii. Angles in a linear pair which are not supplementary.iii. Complementary angles that do not form a linear pair.iv. Adjacent angles which are not in linear pair.v. Angles which are neither complementary nor adjacent.vi. … Read more

Question 1.Name the pairs of opposite rays in the figure alongside. Solution: Question 2.Are the ray PM and PT opposite rays? Give reasons for your answer.Solution:No.Ray PM and Ray PT do not form a straight line and hence are not opposite rays. Intext Questions and Activities Question 1.Observe the adjacent figure and answer the following … Read more

Question 1.Write the measures of the supplements of the angles given below:i. 15°ii. 85°iii. 120°iv. 37°v. 108°vi. 0°vii. a°Solution:i. Let the measure of the supplementary angle be x°.∴ 15 + x = 180∴ 15 + x – 15 = 180 – 15….(Subtracting 15 from both sides)∴ x = 165∴ The measures of the supplement of … Read more

Question 1.The measures of some angles are given below. Write the measures of their complementary angles.i. 40°ii. 63°iii. 45°iv. 55°v. 20°vi. 90°vii. x°Solution:i. Let the measure of the complementary angle be x°.∴ 40 + x = 90∴ 40 + x – 40 = 90 – 40….(Subtracting 40 from both sides)∴ x = 50∴ The measure … Read more

Question 1.Observe the figure and complete the table for ∠AWB. Points in the interior Points in the exterior Points on the arms of the angles Solution: Points in the interior point C, point R, point N, point X Points in the exterior point T, point U, point Q, point V, point Y Points on the … Read more

Question 1.Choose the right option.i. The HCF of 120 and 150 is __(A) 30(B) 45(C) 20(D) 120Solution:(A) 30 Hint:120 = 2 x 2 x 2 x 3 x 5150 = 2 x 3 x 5 x 5∴ HCF of 120 and 150 = 2 x 3 x 5 = 30 ii. The HCF of this … Read more

Question 1.Find the LCM:i. 12, 15ii. 6, 8, 10iii. 18, 32iv. 10, 15, 20v. 45, 86vi. 15, 30, 90vii. 105, 195viii. 12,15,45ix. 63,81x. 18, 36, 27Solution:i. 12, 15 ∴ LCM of 12 and 15 = 3 x 2 x 2 x 5= 60 ii. 6, 8, 10∴ LCM of 6, 8 and 10 = 2 … Read more

Question 1.i. 25, 40ii. 56, 32iii. 40, 60, 75iv. 16, 27v. 18, 32,48vi. 105, 154vii. 42, 45, 48viii. 57, 75, 102ix. 56, 57x. 777, 315, 588Solution:i. 25, 40 ∴ 25 = 5 × 540 = 2 × 2 × 2 × 5∴ HCF of 25 and 40 = 5 ii. 56, 32∴ 56 = 2 … Read more

Question 1.Factorize the following numbers into primes:i. 32ii. 57iii. 23iv. 150v. 216vi. 208vii. 765viii. 342ix. 377x. 559Solution:i. 32 ∴ 32 = 2 × 2 × 2 × 2 × 2 ii. 57∴ 57 = 3 × 19 iii. 23∴ 23 = 23 × 1 iv. 150∴ 150 = 2 × 3 × 5 × 5 … Read more