9514 1404 393
Answer:
- arc AB = 60°
- arc BC = 78°
- arc EF = 40°
- angle AFB = 30°
Step-by-step explanation:
The relevant relations are ...
- the measures of an arc and its central angle are the same
- the sum of the arcs of a circle is 360°
- the measure of an inscribed angle is half the measure of the arc it intercepts
__
Arc AB has the measure of central angle AOB, 60°.
Arc EF has double the measure of inscribed angle EAF, so is 40°.
Arc BC completes the circle, so has measure ...
arc BC = 360° -arc FA -arc AB -arc CE -arc EF
arc BC = 360° -140° -60° -42° -40°
arc BC = 78°
Angle AFB is half the measure of arc AB, so is 60°/2 = 30°.
