Question

(21) In the adjoining figure, sides QP and RQ of APQR are produced to points S and
T respectively. If ZSPR = 135º and. ZPQT = 110° find ZPRQ.​

Answer 1

$\huge\bf \color{green} \mathfrak{Question : - }$

In the adjoining figure, sides QP and RQ of ∆PQR are produced to points S and T respectively. If Angle SPR = 135º and. Angle PQT = 110° find Angle PRQ.

$\huge \bf \color{blue} \mathfrak{Solution : - }$

Angle SPR = 135° •••(Given)

Angle PQT = 110° •••(Given)

Angle PQT + Angle PQR

= 180° •••(Linear Pair)

→ 110° + Angle PQR = 180°

→ Angle PQR = 180° - 110°

→ Angle PQR = 70° •••(1)

Angle QPR + Angle SPR

= 180° •••(Linear Pair)

→ Angle QPR + 135° = 180°

→ Angle QPR = 180° - 135°

→ Angle QPR = 45° •••(2)

Angle PQR + Angle QPR + Angle PRQ

= 180° •••(Angle Sum Property of Triangle)

→ 70° + 45° + Angle PRQ = 180°

→ 115° + Angle PRQ = 180°

→ Angle PRQ = 180° - 115°

→ Angle PRQ = 65°

$\huge \bf \color{orange} \mathfrak{Answer : - }$

Angle PRQ = 65°