Question

Given diameters EB and FC, find the measure of arc EF. *

Answer 1

Correct option: first one -> 45°

Explanation:

FC is a diameter, so the arc FBC measures 180°.

If we have that FBC = FB + BC, then we can find the value of BC:

FB + BC = 180

135 + BC = 180

BC = 45°

If we call the center of the circle 'O, we have that the central angle EOF and the central angle BOC are vertically opposite angles, so EOF = BOC.

The central angles have the same measure that the arcs they are related, so we have that:

angle BOC = arc BC = 45°

angle BOC = angle EOF

angle EOF = arc EF = 45°

Correct option: first one