Question

5. Find the following unknown angles:

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Answer 1

Left image

Though not specifically mentioned in the question, I assume that O is the centre of the circle and AB is a diameter.

Property: a diameter of a circle subtends an angle of 90° at any point on circle outside diameter..

thus, angles C and D are 90°

so, y = 90°

z = 60° ( vertically opposite angle)

60° angle is also the exterior angles of the triangle which is common between ∆ABC and ∆ ABD

thus

x + 15° = 60°

x = 60° - 15°

x = 45°

Right image

it is rather easy, diameter making an angle of 90° at C.

x = 180° - (90 + 39)

x = 180° - 129°

x = 51°