Question

In the given figure, ABCD is a cyclic quadrilateral. the angle bisector of ∠D and ∠C meets at point E. If the ∠DEC = 72∘, then find the value of (α + β).

 

• A. 208∘
• B. 216∘
• C. 108∘
• D. 72∘

Answer 1

Answer:

B. 216∘

∠EDC + ∠DCE + ∠DEC = 180 x + y + 72∘ = 180 x + y = 108 quadrilateral is a cyclic quadrilateral, 2x + 180∘ - β = 180∘ 2x = β 2y + 180∘ - α = 180∘ 2y = α α + β = 2x + 2y α + β = 2 × (x + y) α + β = 2 × (108∘) α + β = 216∘