Respuesta :
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°
