Question

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

Answer 1

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

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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°.