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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