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.
[tex]$m \angle X =\frac{1}{2}({arc \ CD}-{arc} \ AB)[/tex]
[tex]$ 11^\circ =\frac{1}{2}({arc} \ CD-{18^\circ})[/tex]
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.
