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3 years ago

Circles and angles/arcs could someone help me with this geometry question please?

Mathematics

1 answer:

Elden [556K]3 years ago

3 0

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°.

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