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3 years ago

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

Mathematics

1 answer:

SVEN [57.7K]3 years ago

5 0

Answer:

64°
116°
26°
154°
32°

Step-by-step 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°

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°

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Step-by-step explanation:

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*You don't need to show this part on paper*

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