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

Answer:

$m\angle GET=67^o$

Step-by-step 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

$m\angle GET=\frac{1}{2}[arc\ TN-arc\ TG]$

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

$m\angle GET=\frac{1}{2}[180^o-46^o]=67^o$