Question

I need help with these questions(see image).

Please show workings.​

Answer 1

see explanation

Explanation:

(a)

The angle around the centre O of the circle = 360°, then

∠ AOB = 360° - 260° = 100°

Δ AOB is isosceles ( the radii OA and OB are congruent )

The altitude from O bisects ∠ AOB , thus

y = 50°

Since the triangle is isosceles the 2 base angles are congruent, so

x =
`(180-100)/(2)` =
`(80)/(2)` = 40°

(b)

∠ POR = 360° - 254° = 106°

Δ POR is isosceles (the radii OP and OR are congruent ) , then

the 2 base angles are congruent , thus

a =
`(180-106)/(2)` =
`(74)/(2)` = 37°