Q. 234.7( 27 Votes )
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.
Answer :
Method 1:
It is given in the question that:
∠SPR = 135O
And,
∠PQT = 110o
Now, according to the question,
∠SPR + ∠QPR = 180O (SQ is a straight line)
135o + ∠QPR = 180O
∠QPR = 45O
And,
∠PQT + ∠PQR = 180O (TR is a straight line)
110o + ∠PQR = 180O
∠PQR = 70O
Now,
∠PQR + ∠QPR + ∠PRQ = 180O (Sum of the interior angles of the triangle)
70o + 45o + ∠PRQ = 180O
115O + ∠PRQ = 180O
∠PRQ = 65O
Method 2:
It is given in the question that:
∠SPR = 135O
And,
∠PQT = 110o
∠PQT + ∠PQR = 180O (TR is a straight line)
110o + ∠PQR = 180O
∠PQR = 70O
Now, we know that the exterior angle of the triangle equals the sum of interior opposite angles. Therefore,
∠SPR = ∠PQR + ∠PRQ
135o = 70o + ∠PRQ
∠PRQ = 65o
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