Question

the circle below has center T. suppose that m UV = 138 degrees and that UW is tangent to the circle at U. find the following

Answer 1

Angle UTV is basically given: it's 138°.

Moreover, since UTV is isosceles, the other two angles have the same measure x. We thus have

$138+x+x=180 \iff 2x=42 \iff x=21$

So, TUV is 21°, and VUW is complementary, so it must be 69° so that they sum up to 90°