Question

I need help with these questions(see image). Please show workings.​

Answer 1

Answer:

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 = \frac{180-100}{2}

2

180−100

= \frac{80}{2}

2

80

= 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 = \frac{180-106}{2}

2

180−106

= \frac{74}{2}

2

74

= 37°

Answer 2

Answer:

see explanation

Step-by-step 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 = $\frac{180-100}{2}$ = $\frac{80}{2}$ = 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 = $\frac{180-106}{2}$ = $\frac{74}{2}$ = 37°