Question

Please help me in this question.
Find angle x°,y°,z°.

Answer 1

x = 22

y = 26

z = 48

Explanation:

ΔSPR is isosceles, meaning two angles are equal, as indicated.

one base angle is 66, meaning the other one is also 66.

alternate angles are equal ; angle Q = angle S = 22 = x

To find the other angle of the triangle below, add 22 and 66 and subtract from 180 to get 92.

vertically opposite angles are equal ; 92

88 88

92

the triangle on the upper right has 92, 22, and the missing angle which is 66.

the upper left triangle has 88, 66 and the missing which is 26 = y

the straight line above(PQ), now has 66, 66 and the missing one .add , then take away from 180 to get 48 = z

Answer 2

x = 22°

y = 26°

z = 48°

Explanation:

∠PQS and ∠QSR is a pair of alternate interior angles

plus PQ is parallel to SR

then

x = 22°

SPR is an isosceles triangle then m∠PRS = 66°

Therefore x + y = 180-(66+66) = 180-132 = 48

then y = 48 - x = 48-22 = 26

finally, z = x + y = 48