1) given: mlhe=84°

find: m∠eyl.

2)given: m∠eyl=72°
find: m arc ehl, m arc lve

Part 1) The measure of angle EYL is

Part 2) The measure of arc EHL is and the measure of arc LVE is

Step-by-step explanation:

we know that

The measurement of the outer angle is the semi-difference of the arcs which comprises

Part 1)

Let

x------> the measure of arc LHE

y----> the measure of arc LVE

we know that

Find the value of y

Find the measure of angle EYL

substitute the values

Part 2)

Let

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

y----> the measure of arc LVE

we know that

-----> equation A

substitute

--------> equation B

equate equation A and equation B and solve for y

Find the value of x

therefore

The measure of arc EHL is

The measure of arc LVE is

a is the right answer