On circle O below, ZX is a diameter. The measure of ZY is 104°
What is the measure of OZY?

Circle And Triangle

The Angle ∠OZY is 38°

Step-by-step explanation:

Given ZX is the diameter of the circle.

Given ∠ZOY is 104°

Since OX ,OZ and OY are the radius of the Circle with Center O

So OX = OZ = OY

So the ΔOZY is an isosceles triangle as OZ = OY

Sum of angles of the triangle ΔOZY = 180°

Since the ΔOZY is an isosceles triangle as OZ = OY,

so ∠OZY= ∠OYZ

∠OZY + ∠OYZ + ∠ZOY = 180° (Sum of angles of ΔOZY)

⇒ ∠OZY + ∠OYZ + 104° = 180°

⇒ ∠OZY + ∠OYZ = 180° - 104°

⇒ ∠OZY + ∠OYZ = 76°

⇒ ∠OZY + ∠OZY = 76°  ( As ∠OZY= ∠OYZ )

⇒ 2 × ∠OZY = 76°

⇒ ∠OZY = 76°/2 = 38°

Hence the ∠OZY is 38°

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