Given: m∠eyl=72°
find: mehl , mlve

Part 1) The measure of arc EHL is

Part 2) The measure of angle LVE is

Step-by-step explanation:

step 1

Let

x-----> the measure of arc EHL

y----> the measure of arc EVL

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

so

we have

substitute

------> equation A

Remember that

-----> equation B ( complete circle)

substitute equation A in equation B and solve for x

Find the value of y

therefore

The measure of arc EHL is

The measure of arc EVL is

step 2

Find the measure of angle LVE

we know that

The inscribed angle measures half that of the arc comprising

Let

x-----> the measure of arc EHL

we have

substitute