Question

please answer it fast

Answer 1

PQRS is quadiratral
so,
angle SPQ + angle RQP+ 50+110=360
2(angle APQ+angle AQP )=200
angle APQ+ angle AQP=100
for triangle APQ
angle PAQ=180-100=80

Answer 2

Given : A Quadrilateral ABCD , with ∠R = 110° , ∠S = 50°

To find : Measure of ∠PAQ.

As , PQRS is a quadrilateral , the angle sum of all the angles in it is 360°.
i.e ,
∠S + ∠R + ∠SPQ+ ∠ PQR = 360°
110° + 50°+ ∠SPQ+ ∠ PQR = 360°
∠SPQ+ ∠ PQR = 360° - (110 + 50)
∠SPQ+ ∠ PQR = 200 ° .................(1)

But ,
∠ APQ = 1/2 ∠SPQ
∠AQP = 1/2 ∠ PQR

∴ From (1) ,
1/2 ∠SPQ + 1/2 ∠ PQR = 100
i.e ,
∠ APQ + ∠AQP = 100°


In Δ PAQ ,
∠PAQ + ∠ APQ + ∠AQP = 180 ° [ Angle sum property of a Δ ]

∠PAQ + 100° = 180°
∠PAQ = 180° - 100°
∴ ∠PAQ = 80°


Please mark brainliest ...