Answer:
The measure of angle YUV is 40°
Step-by-step explanation:
Consider the diagram of this question is attached below,
Where, Tangent line UV and secant XY intersect outside the circle at U,
Since,
[tex]\widehat{XV}+\widehat{XY}+\widehat{VY}=360^{\circ}[/tex]
We have,
[tex]\widehat{XV}=80^{\circ}, \widehat{XY}=120^{\circ}[/tex]
[tex]\implies 80^{\circ}+120^{\circ}+\widehat{VY}=360^{\circ}[/tex]
[tex]200^{\circ}+\widehat{VY}=360^{\circ}[/tex]
[tex]\widehat{VY}=360^{\circ}-200^{\circ}=160^{\circ}[/tex]
Since, the measure of intercepted angle outside the circle is half of the difference of measure of intercepted arcs,
[tex]\implies m\angle YUV = \frac{\widehat{VY}-\widehat{XV}}{2}[/tex]
[tex]=\frac{160^{\circ}-80^{\circ}}{2}[/tex]
[tex]=\frac{80^{\circ}}{2}[/tex]
[tex]=40^{\circ}[/tex]
