Question

Triangle XYZ is equilateral with vertices located on circle W.

Answer 1

Answer:

$m\ arc\ YZ=120^o$

$m\angle YWZ=120^0$

Step-by-step explanation:

we know that

An equilateral triangle has three equal sides and three equal interior angles. The measure of each interior angle is equal to 60 degrees.

step 1

Find the measure of arc YZ

Remember that

The inscribed angle is half that of the arc comprising

so

In this problem

$60^o=\frac{1}{2}[m\ arc\ YZ]$

$m\ arc\ YZ=(60^o)(2)=120^o$

$m\ arc\ YZ=m\ arc\ XZ=m\ arc\ XY$

step 2

Find the measure of angle YWZ

we know that

$m\angle YWZ=m\ arc YZ$ -----> by central angle

therefore

$m\angle YWZ=120^0$

see the attached figure to better understand the problem

Answer 2

Step-by-step explanation:

myz = 120° & mZYWZ = 120°