Question

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


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Thank u :)
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Answer 1

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Given:

• ∠SPR = 135° and ∠PQT = 110°

To find:

• ∠PRQ

`\leadsto`According to Angle sum property of a triangle , sum of the interior angles of a triangle is 180°.

➱ ∠SPR + ∠QPR = 180° [Linear pair]

➱ 135° + ∠QPR = 180°

➱ ∠QPR = 180° - 135°

➱ ∠QPR = 45°.....(i)

➱ ∠PQT + ∠PQR = 180° [Linear pair]

➱ 110° + ∠PQR = 180°

➱ ∠PQR = 180° - 110°

➱ ∠PQR = 70°.....(ii)

Now,

➛ ∠PQR + ∠QPR + ∠PRQ = 180° [Angle sum property of a triangle]

➱ 70°+ 45° + ∠PRQ = 180° [from (i) and (ii)]

➱ ∠PRQ = 180° - 115°

➥ ∠PRQ = 65°

hope it's help u!! :D