Question

If arc XV = 80° and arc YX = 120°, what is the measure of ?YUV?

Answer 1

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,

$\widehat{XV}+\widehat{XY}+\widehat{VY}=360^{\circ}$

We have,

$\widehat{XV}=80^{\circ}, \widehat{XY}=120^{\circ}$

$\implies 80^{\circ}+120^{\circ}+\widehat{VY}=360^{\circ}$

$200^{\circ}+\widehat{VY}=360^{\circ}$

$\widehat{VY}=360^{\circ}-200^{\circ}=160^{\circ}$

Since, the measure of intercepted angle outside the circle is half of the difference of measure of intercepted arcs,

$\implies m\angle YUV = \frac{\widehat{VY}-\widehat{XV}}{2}$

$=\frac{160^{\circ}-80^{\circ}}{2}$

$=\frac{80^{\circ}}{2}$

$=40^{\circ}$