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pantera1 [17]
3 years ago
8

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

Mathematics
1 answer:
SCORPION-xisa [38]3 years ago
3 0

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\°

<em>Find the measure of angle EYL</em>

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\°

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