# If in ∆PQR, ∠ P = 120 o, PS ⊥ QR at S and PQ + QS = SR, then the measu

| If in ∆PQR, ∠P = 120

^{o}, PS ⊥ QR at S and PQ + QS = SR, then the measure of ∠Q is :A. 40^{o}

B. 50^{o}

C. 20^{o}

D. 30^{o}

### Right Answer is: A

#### SOLUTION

Let

We construct a line PD which meets QR at D and (Let).

Since,

In ∆ PQR, PS ⊥ QD,

Then it will be an isosceles triangle.

Then,

In ∆ PRD,

PR = PD

(Let)

Then (external angle)

We know that in ∆ PQD,

(given)

Required,

∠Q = 2θ = 40°

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If in ∆PQR, ∠ P = 120 o, PS ⊥ QR at S and PQ + QS = SR, then the measu