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35 votes
35 votes
What is the measure of ∠C?

What is the measure of ∠C?-example-1
User Dayanna
by
2.4k points

2 Answers

15 votes
15 votes

Answer: 38 degrees

Explanation:

Because arc AB is equal to 76 degrees, angle ADB must also be 76 degrees.

Then simply take the supplement of the angle to get that < CDA is 104 degrees. Because it is part of an isosceles triangle, simply subtract 104 from 180 to get that <A + <C = 74 degrees. Because triangle ADC is isosceles (All radii of a circle are equal), simply divide 76 / 2 to get that <C = 38.

Hope it helps :)

User John Blackberry
by
3.3k points
14 votes
14 votes


\qquad \qquad\huge \underline{\boxed{\sf Answer}}

Theorem : Angle subtended by an arc on the circumference of the circle is half the angle subtended by the same arc on the center of the same circle.

That is :


\qquad \sf&nbsp; \dashrightarrow \: \angle \: c = (1)/(2) * 76


\qquad \sf&nbsp; \dashrightarrow \: \angle \: c = 38 \degree

User Sunriser
by
3.2k points
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