Question

Find the measure of the are or angle indicated. Assume that lines which appear tanget are tangents​

Answer 1

Given:

On a circle, UT and UV are two tangent

Measure of arc VT = 125 degrees.

To find:

The measure of angle TUV.

Solution:

Intersecting tangents theorem: According to this theorem, if two tangent are drawn to the circle then the measure of angle on the intersection is half of the difference of intercepted major arc and minor arc.

We know that the measure of complete arc of a circle is 360 degrees. So,

$\text{Major arc}(VT)=360^\circ -\text{Minor arc}(VT)$

$\text{Major arc}(VT)=360^\circ -125^\circ$

$\text{Major arc}(VT)=235^\circ$

Using Intersecting tangents theorem, we get

$m\angle TUV =\dfrac{1}{2}(\text{Major arc}(VT)-\text{Minor arc}(VT))$

$m\angle TUV =\dfrac{1}{2}(235^\circ -125^\circ )$

$m\angle TUV =\dfrac{1}{2}(110^\circ )$

$m\angle TUV =55^\circ$

Therefore, the measure of angle TUV is 55 degrees.