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If Fig. 6.39 ,sides QP and …

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If Fig. 6.39 ,sides QP and RQ of ? PQR are produced to points S and T respectively. If angle = 135 and angle PQT = 110, Find angle PQR

Posted by Aryansh Singh 5 years, 2 months ago

CBSE > Class 09 > Mathematics

1 answers

Gaurav Seth 5 years, 1 month ago

∵ TR is a line
∴ ∠PQT + ∠PQR = 180°
⇒    110° + ∠PQR = 180°
⇒ ∠PQR = 180° - 110° = 70°    ...(1)
∵ QS is a line
∴ ∠SPR + ∠QPR = 180°
⇒    135° + ∠QPR = 180°
⇒ ∠QPR = 180° - 135° = 45° ...(2)
In ∆PQR,
∠PQR + ∠QPR + ∠PRQ = 180°
| ∵ The sum of all the angles of a triangle is 180°
⇒ 70° + 45° + ∠PRQ = 180°
| Using (1) and (2)
⇒    115° + ∠PRQ = 180°
⇒ ∠PRQ = 180° - 115° = 65°.

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