In Fig. 6.39, sides QP and RQ of Δ PQR are produced to points S and T respectively. If ∠ SPR = 135° and ∠ PQT = 110°, find ∠ PRQ.

Question

In Fig. 6.39, sides QP and RQ of &#x394; PQR are produced to points S and T respectively. If &#x2220; SPR = 135&#xB0; and &#x2220; PQT = 110&#xB0;, find &#x2220; PRQ.

Philoid · Accepted Answer

It is given in the question that:

∠SPR = 135^O

And,

∠PQT = 110^o

Now, according to the question,

∠SPR + ∠QPR = 180^O (SQ is a straight line)

135^o + ∠QPR = 180^O

∠QPR = 45^O

And,

∠PQT + ∠PQR = 180^O (TR is a straight line)

110^o + ∠PQR = 180^O

∠PQR = 70^O

Now,

∠PQR + ∠QPR + ∠PRQ = 180^O (Sum of the interior angles of the triangle)

70^o + 45^o + ∠PRQ = 180^O

115^O + ∠PRQ = 180^O

∠PRQ = 65^O