Question

5. In quadrilateral PQRS, PQ = PS, find the measures of angles x and y.

Answer 1

Answer:

PQ = PS

Therefore, ANGLE PQS= ANGLE PSQ= x

In triangle PQS

ANGLE QPS + ANGLE PQS+ ANGLE PSQ = 180° (Sum of angles of a triangle is 180°)

112° + x + x = 180°

2x = 180-112

2x= 68°

x = 68/2 = 34

ANGLE PQS = ANGLE PSQ = 34 °

In triangle QRS

ANGLE RQS + ANGLE QRS + ANGLE QSR = 180°

80 + 57 + ANGLE QSR = 180

ANGLE QSR = 180 - 80 - 57 = 43°

y = ANGLE PSQ + ANGLE QSR

= 34 + 43 = 77°