Question

In ∆PQR the measures of ∠P and ∠Q are equal and m∠PRQ = 70°, Find the measures of the following angles.

1. m∠PRT 

2. m∠P 

3. m∠Q

Answer 1

Here, ∠PRQ and ∠PRT are angles in a linear pair. 

m∠PRQ + m∠PRT = 180° 

∴ 70 + m∠PRT = 180 

∴ m∠PRT = 180 – 70 

∴ m∠PRT = 110° 

Now, ∠PRT is the exterior angle of ∆PQR. 

∴ m∠P + m∠Q = m∠PRT 

∴ m∠P + m∠P = m∠PRT 

….(The measures of ∠P and ∠Q is same) 

∴ 2m∠P = 110

∴ m∠P = 110/2

∴ m∠P = 55° 

∴ m∠Q =