In the given figure sides QP and RQ of ∠PQR are produced to points S

1.	In the given figure sides QP and RQ of ∠PQR are produced to points S and T respectively. If ∠SPR = 135° and ∠PQT = 110°, find ∠PRQ.
Answer» Given that ∠SPR = 135° and ∠PQT =110° From the figure ∠SPR + ∠RPQ = 180° ∠PQT + ∠PQR = 180° [∵ linear pair of angles] ⇒ ∠RPQ = 180° – ∠SPR = 180° – 135° = 45° ⇒ ∠PQR = 180° – ∠PQT = 180°-110° = 70° Now in APQR ∠RPQ + ∠PQR + ∠PRQ = 180° [∵ angle sum property] ∴ 45° + ’70° + ∠PRQ = 180° ∴ ∠PRQ = 180°-115° = 65°

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

Answer»

Given that ∠SPR = 135° and ∠PQT =110°

From the figure

∠SPR + ∠RPQ = 180°

∠PQT + ∠PQR = 180°

[∵ linear pair of angles]

⇒ ∠RPQ = 180° – ∠SPR = 180° – 135° = 45°

⇒ ∠PQR = 180° – ∠PQT = 180°-110° = 70°

Now in APQR

∠RPQ + ∠PQR + ∠PRQ = 180°

[∵ angle sum property]

∴ 45° + ’70° + ∠PRQ = 180°

∴ ∠PRQ = 180°-115° = 65°