In ΔPQR, the side QR is exten

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Geometry

Question:

In ΔPQR, the side QR is extended to S such that RS = PR. If ∠QPS = 110° and ∠PRQ = 70°, then the value of ∠PQR is :

Options:

50°

40°

35°

45°

Correct Answer:

35°

Explanation:

We have,

RS = PR

∠QPS = 110°

∠PRQ = 70°

∠PSR = ∠RPS = x [RS = PR]

Now, We know that,

∠PRQ = ∠PSR + ∠RPS

= 70° = 2x

= x = 35°

So, ∠QPR = 110° - 35° = 75°

∠PQR = 180° - (75° + 70°) = 180° - 145° = 35°