Question

In the diagram, PQ=PR=QS and angle
QPR= 20°. What is the size of angle
RQS ?​

Answer 1

In the diagram, PQ=PR=QS and angle QPR= 20°. What is the size of angle RQS ?

In the given figure triangle PQR is isosceles triangle.

Hence, angle PQR = PRQ

Now,

20°+PQR+PRQ = 180°

or, 2 PQR = 160°

or, PQR = 80°

Hence, PQR = PRQ = 80°

Again,

Angle QRS = 180°- 80°

= 100°

In triangle PQS,

QPR+QSP+PQR+RQS = 180°

or, 20°+80°+RQS+QSR = 180°

or, 100°+20°+RQS = 180°

[since PQ = QS angles QPR.

= QSR = 20°]

or, RQS = 60°

Hence, RQS is 60°.

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