Find QPS in the diagram.

Correct Answer is : 40∘40^{}40∘

Correct Answer is : 40∘40^{}40∘

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BECE Mathematics 2019 Paper

Question : 20

Total: 40

\angle QPS

Solution:

Concept:

Use properties of isosceles triangles and the angle sum of a triangle.

Explanation:

\triangle QSR

, the base angles are equal:

\angle SQR = \angle QRS = 35^\circ

Using angle sum property of a triangle:

35^\circ + 35^\circ + \angle RSQ = 180^\circ

\angle RSQ = 180^\circ - 70^\circ = 110^\circ

Since

\angle RSQ

and

\angle QSP

form a straight line:

110^\circ + \angle QSP = 180^\circ

\angle QSP = 70^\circ

\triangle QPS

, it is isosceles with

\angle SQP = \angle QSP = 70^\circ

Thus:

70^\circ + 70^\circ + \angle QPS = 180^\circ

\angle QPS = 180^\circ - 140^\circ = 40^\circ

Answer:

\angle QPS = 40^\circ

(Option B).

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