Question

in a quadrilateral pqrs angle p + angle r= 2 times angle q + angle s . if angle p is equal to 140 and angle s = 60 .find the angle q​

Answer 1

Answer:

By angle sum property of a quadrilateral,

∠P+∠Q+∠R+∠S=360

∘

⇒50

∘

+50

∘

+60

∘

+∠S=360

∘

⇒∠S = 200

∘

Here, we can see that ∠S is greater than 180

∘

which implies that the quadrilateral PQRS is concave.

Answer 2

$∠P + ∠R = 2(∠Q+∠S)$

$P= 140 , S \: = 60$

$140 + ∠R = 2(∠Q+60)$

$140 + ∠R = ∠Q+120$

$140 - 120 = ∠R \: and \: ∠Q$

$∠Q = 20$