Question

What is the measure of arc CD?

Answer 1

Option C:

The measure of arc CD is 40°.

Solution:

Given data:

m∠X = 11° and m(arc AB) = 18°

To find the measure of arc CD:

We know that,

Angle formed by two intersecting secants outside the circle is equal to half of the difference between the intercepted arcs.

$m \angle X =\frac{1}{2}({arc \ CD}-{arc} \ AB)$

$11^\circ =\frac{1}{2}({arc} \ CD-{18^\circ})$

Multiply by 2 on both sides.

22° = arc CD - 18°

Add 18° from both sides.

40° = arc CD

Switch the sides.

arc CD = 40°

Hence the measure of arc CD is 40°.

Option B is the correct answer.