Question

1) Given: mLHE=84°Find: m∠EYL. 2)Given: m∠EYL=72°Find: m arc EHL, m arc LVE

Answer 1

Answer:

Part 1) The measure of angle EYL is $96\°$

Part 2) The measure of arc EHL is $108\°$ and the measure of arc LVE is $252\°$

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

$x+y=360\°$

$x=84\°$

Find the value of y

$y=360\°-84\°=276\°$

Find the measure of angle EYL

$m$

substitute the values

$m$

Part 2)

Let

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

y----> the measure of arc LVE

we know that

$x+y=360\°$

$x=360\°-y$ -----> equation A

$m$

$m$

substitute

$72\°=\frac{1}{2} (y-x)$

$144\°=(y-x)$

$x=y-144\°$ --------> equation B

equate equation A and equation B and solve for y

$360\°-y=y-144\°$

$2y=360\°+144\°$

$2y=504\°$

$y=252\°$

Find the value of x

$x=252\°-144\°=108\°$

therefore

The measure of arc EHL is $108\°$

The measure of arc LVE is $252\°$