What theorem is applicable?

Geometry Level 2

Shown above is a circle with center at O O . Find ϕ \phi (in degrees).

More problems

3 0 ∘ 30^\circ 4 5 ∘ 45^\circ 2 0 ∘ 20^\circ 4 0 ∘ 40^\circ

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1 solution

By Thale’s Theorem (inscribed angle),

∠ B A C = 1 2 ( 50 ) = 25 \angle BAC=\dfrac{1}{2}(50)=25

∠ A B D = 1 2 ( 30 ) = 15 \angle ABD=\dfrac{1}{2}(30)=15

By Exterior Angle Theorem,

ϕ = 15 + 25 = \phi=15+25= 4 0 ∘ \boxed{40^\circ}

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