Question

Please write down your work on the loose leaf, take a CLEAR picture, and upload here. Thank you.

Answer 1

m(∠C) = 18°

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) =
`(1)/(2)[\text{arc(EA)}-\text{arc(BD)}]`

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) =
`(1)/(2)(56^(\circ)-20^(\circ))`

m(∠C) = 18°