Question

Given that AB is a diameter of circle O, find the missing angle and are measures.

Answer 1

• 64°
• 116°
• 26°
• 154°
• 32°

Explanation:

The relevant relations are ...

• an arc has the same measure as the central angle it subtends
• angles of a linear pair are supplementary (total 180°)
• an inscribed angle has half the measure of the arc it subtends
• the total of arcs of a circle is 360°; of a semicircle, 180°

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arc CB has the measure of central angle COB: 64°

angle AOC is the supplement of angle COB: 180° -64° = 116°

arc AD is twice the measure of inscribed angle ABD: 2×13° = 26°

arc DFB is the supplement of arc AD: 180° -26° = 154°

angle CDB is half the measure of arc CB: 64°/2 = 32°