Geometry Practice Test 6

Question : 18 of 39

Marks: +1, -0

Find ∠ROQ. In DPQR, ∠P = 60°, if side PQ and PR are produced to S and T such that the angle bisector of ∠RQS and ∠QRT meet at O in the given figure.

Solution:

In ΔPQR,
∠P + ∠PQR + ∠QRP = 180°
60° + (180 - 2∠1) + (180 - 2∠2) = 180°
420 - 2∠1 - 2∠2 = 180 °
420 - 180 = 2(∠1 + ∠2)

{240}/2

= ∠1 + ∠2
So, ∠1 + ∠2 = 120° ......(i)
In ΔQOR,
∠1 + ∠2 + ∠ROQ = 180°
120 + ∠ROQ = 180° [Using eq (i)]
∠ROQ = 180 - 120
∠ROQ = 60°

Go to Question:

Prev Question

Next Question