Question

In Δ PQR, ∠P= 120° , PS⊥QR at Sand PQ+QS=SR , then the measure of ∠Q.

Answer 1

The answer will be 30°....

Hope this helps you...

Answer 2

measure of ∠Q is 40°

Step-by-step explanation:

let PQ =  x

QS = y

ST = QS = y

in triangle PQT

PS ⊥ QT , QS = ST

Therefore , PQT is an isosceles triangle

now , PQ= PT = x = TR

PTR is also a isosceles triangle

let

$\angle PTQ = 2\theta \\\\\angle R = \theta$

therefore ,

$\angle QPT = 180-(2\theta +2\theta)\\\\= 180-(4\theta)\\\\now, \\\\\angle QPR = \angle QPT + \angkle TPR \\\\120 = 180 - 4\theta +\theta \\\\theta = 20^\circ \\\\now, \\\\\angle PQT = 2\theta = 2\times 20 = 40^\circ \\\\\angle Q = 40^\circ$

hence , measure of ∠Q is 40°

#Learn more :

PQR is a right triangle right angled at Q and QS perpendicular to PR. If PQ=10cm and PS=8cm. Find QS ,SR and QR

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