Question

What is m CD ? Plzz help

Answer 1

Given:

Arc(AB) = 78 degrees

Measure of angle CMD = 106 degrees

To find:

The measure of arc CD.

Solution:

Secant intersection theorem: If two secant of a circle intersect each other inside the circle, then the intersection angle is the average of intercepted arcs.

Using secant intersection theorem, we get

$m\angle CMD=\dfrac{1}{2}(Arc(AB)+Arc(CD))$

$106^\circ=\dfrac{1}{2}(78^\circ+Arc(CD))$

Multiply both sides by 2.

$212^\circ=78^\circ+Arc(CD)$

$212^\circ-78^\circ=Arc(CD)$

$134^\circ=Arc(CD)$

Therefore, the measure of arc CD is 134 degrees and the correct option is C.