Option D:
The measure of angle x is 71 degree.
Solution:
m(ar AB) =92° and m(ar CD) = 50°
The measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
[tex]$\Rightarrow \angle x^\circ =\frac{1}{2} (m (ar AB) + m (ar CD))[/tex]
[tex]$\Rightarrow \angle x^\circ =\frac{1}{2} (92^\circ+50^\circ)[/tex]
[tex]$\Rightarrow \angle x^\circ =\frac{1}{2} \ (142^\circ)[/tex]
[tex]$\Rightarrow \angle x^\circ =71^\circ[/tex]
The measure of angle x is 71 degree.
Option D is the correct answer.
