**Chapter 4 Angles and Pairs of Angles Set 4.6**

Question 1.

Lines AC and BD intersect at point P. mâˆ APD = 47Â° Find the measures of âˆ APB, âˆ BPC, âˆ CPD.

Solution:

âˆ APD and âˆ APB are angles in a linear pair.

âˆ´mâˆ APD + mâˆ APB = 180Â°

âˆ´47 + mâˆ APB = 180

âˆ´47 + mâˆ APB â€“ 47 = 180 â€“ 47 â€¦.(Subtracting 47 from both sides)

âˆ´mâˆ APB = 133Â°

mâˆ CPD = mâˆ APB = 133Â° â€¦ .(Vertically opposite angles)

mâˆ BPC = mâˆ APD = 47Â° â€¦ .(Vertically opposite angles)

âˆ´The measures of âˆ APB, âˆ BPC and âˆ CPD are 133Â°, 47Â° and 133Â° respectively.

Question 2.

Lines PQ and RS intersect at point M. mâˆ PMR = xÂ°.What are the measures of âˆ PMS, âˆ SMQ and âˆ QMR?

Solution:

âˆ PMR and âˆ PMS are angles in a linear pair.

âˆ´ mâˆ PMR + mâˆ PMS = 180Â°

âˆ´ x + mâˆ PMS = 180

âˆ´ mâˆ PMS = (180-x)Â°

mâˆ QMR = mâˆ PMS = (180 â€“ x)Â° â€¦ .(Vertically opposite angles)

mâˆ SMQ = mâˆ PMR = xÂ° â€¦. (Vertically opposite angles)

âˆ´The measures of âˆ PMS, âˆ SMQ and âˆ QMR are (180 â€“ x)Â°, xÂ° and (180 â€“ x)Â° respectively.