Question

What is the measure of ∠C?

Answer 1

Answer: 38 degrees

Step-by-step 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 :)

Answer 2

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

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 :

$\qquad \sf  \dashrightarrow \: \angle \: c = \frac{1}{2} \times 76$

$\qquad \sf  \dashrightarrow \: \angle \: c = 38 \degree$