Angles and Pairs of Angles Class 7 Practice Set 20 Answers Solutions Chapter 4
Question 1
Maharashtra Board Solution
Lines AC and BD intersect at point P. m∠APD = 47° Find the measures of ∠APB, ∠BPC, ∠CPD.
Solution & Step-by-Step Answer:
∠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° ….(Vertically opposite angles) m∠BPC = m∠APD = 47° ….(Vertically opposite angles) ∴The measures of ∠APB, ∠BPC and ∠CPD are 133°, 47° and 133° respectively.
Question 2
Maharashtra Board Solution
Lines PQ and RS intersect at point M. m∠PMR = x°.What are the measures of ∠PMS, ∠SMQ and ∠QMR?
Solution & Step-by-Step Answer:
∠PMR and ∠PMS are angles in a linear pair. ∴ m∠PMR + m∠PMS = 180° ∴ x + m∠PMS = 180 ∴ m∠PMS = (180-x)° m∠QMR = m∠PMS = (180 – x)° ….(Vertically opposite angles) m∠SMQ = m∠PMR = x° …. (Vertically opposite angles) ∴The measures of ∠PMS, ∠SMQ and ∠QMR are (180 – x)°, x° and (180 – x)° respectively.