Question

Line ET is tangent to circle A and T, and the measure of arc TG is 46 degrees. What is the measure of Angle GET

Answer 1

`m\angle GET=67^o`

Explanation:

The picture of the question in the attached figure

we know that

The measure of the external angle is the semi-difference of the arches it covers.

so

`m\angle GET=(1)/(2)[arc\ TN-arc\ TG]`

Remember that the diameter divide the circle into two equal parts

In this problem

TN is a diameter

we have

`arc\ TN=180^o` ----> because is half the circle (TN is a diameter)

`arc\ TG=46^o` ---> is given

substitute

`m\angle GET=(1)/(2)[180^o-46^o]=67^o`