Given:
Measure of intercepted arcs 72° and 22°.
To find:
The value of the variable x.
Solution:
Angle of intersecting secants theorem:
If two chords intersecting outside a circle, then the measure of an angle formed is half of the positive difference of the measure of intercepted arcs.
[tex]$\Rightarrow \angle x^\circ = \frac{1}{2}(72^\circ-22^\circ)[/tex]
[tex]$\Rightarrow \angle x^\circ = \frac{1}{2}(50^\circ)[/tex]
[tex]$\Rightarrow \angle x^\circ = 25^\circ[/tex]
The value of the variable is 25°.
