In a circles with center Q, ZXWQ is a parallelogram where X is a point on the minor arc ZW. What is the measure of ∠ZQW?
Answer & explanation
Correct answer: option 4
Let ∠ZXW = θ
⇒ Opposite angles in parallelogram are equal
Therefore, ∠ZQW = ∠ZXW, ⇒ y = θ
Now,
∠ZQW = 2 ∠ZVW
⇒ y = 2 (180° - θ) (θ = y)
⇒ θ = 360° - 2θ
⇒ 3 θ = 360°
⇒ θ = 120°
⇒ θ = y = 120°