Given:
Consider the below figure attached with this question.
To find:
The measure of angle 3.
Solution:
According to intersecting secant theorem, if two secants of a circle intersect each other outside the circle, then the angle on the intersection is half of the difference of the intercepted arc.
[tex]\text{Angle on intersection}=\dfrac{1}{2}(\text{Major arc}-\text{Minor arc})[/tex]
Using the intersecting secant theorem, we get
[tex]m\angle 3=\dfrac{1}{2}(m(arcXY)-m(arcWZ))[/tex]
[tex]m\angle 3=\dfrac{1}{2}(85^\circ-25^\circ)[/tex]
[tex]m\angle 3=\dfrac{1}{2}(60^\circ)[/tex]
[tex]m\angle 3=30^\circ[/tex]
Therefore, the measure of angle 3 is 30 degrees.
