Question

Bearing........find the marked angles f and g

Answer 1

g = 132° , f = 24°

Explanation:

∠ PRQ = 180° - 114° = 66°

the central angle g is twice the angle subtended at the circumference on the same arc PQ , then

g = 2 × ∠ PRQ = 2 × 66 = 132°

Δ POQ is isosceles , 2 congruent sides , the radii OP and OQ

The base angles of the triangle are congruent , then

f =
`(180-132)/(2)` =
`(48)/(2)` = 24°

Answer 2

Explanation:

g is a central angle for arc PQ

= 2 * segment angle of arc PQ

= 2 * <PRQ

= 2 * (180 - 114)

= 2 * 66

= 132 degree

Drawing is a little confusing about f and assuming f is <PQO

<PQO = <QPO because OPQ is an isosceles triangle

The sum of interior angles of a triangle = 180 degree

f + f + g = 180

2f = 180 - 132 = 48

f = 24 degree

Edit: Thank you, fieryanswererft, for pointing out my mistake!