Answer:
m(∠C) = 18°
Step-by-step explanation:
From the picture attached,
m(arc BD) = 20°
m(arc DE) = 104°
Measure of the angle between secant and the tangent drawn from a point outside the circle is half the difference of the measures of intercepted arcs.
m(∠C) = [tex]\frac{1}{2}[\text{arc(EA)}-\text{arc(BD)}][/tex]
Since, AB is a diameter,
m(arc BD) + m(arc DE) + m(arc EA) = 180°
20° + 104° + m(arc EA) = 180°
124° + m(arc EA) = 180°
m(arc EA) = 56°
Therefore, m(∠C) = [tex]\frac{1}{2}(56^{\circ}-20^{\circ})[/tex]
m(∠C) = 18°
