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

Method 1:
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

Method 2:

It is given in the question that:

∠SPR = 135^O

And,

∠PQT = 110^o

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

110^o + ∠PQR = 180^O

∠PQR = 70^O

Now, we know that the exterior angle of the triangle equals the sum of interior opposite angles. Therefore,
∠SPR = ∠PQR + ∠PRQ
135^o = 70^o + ∠PRQ
∠PRQ = 65^o