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Work out the size of angle y.

Work out the size of angle y.-example-1
User Minimo
by
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1 Answer

2 votes

Answer:

y = 32°

Explanation:

The central angle is twice the angle on the circle subtended by the same arc

∠ BOC = 2 × ∠ BAC , that is

x + 62 = 2(2x - 50) ← distribute

x + 62 = 4x - 100 ( subtract x from both sides )

62 = 3x - 100 ( add 100 to both sides )

162 = 3x ( divide both sides by 3 )

54 = x

Then

∠ BOC = x + 62 = 54 + 62 = 116°

Δ BOC is isosceles ( OB = OC ) so the 2 base angles are congruent

y =
(180-116)/(2) =
(64)/(2) = 32°

User Fiyaz Hasan
by
4.5k points