Answer:
m(ARC)EHL: 108°
m(ARC)LVE: 252°
Explanation:
Hey, so initially, we should start off with some stuff:
The sum of the arcs add up to 360°
m∠EYL=72°
We can create a system and use substitution to find the measure of an arc we don't know.
Step 1: We can use the 'Secants exterior angle theorem' to help us find the measure of (ARC)EHL.
<EYL=1/2((ARC)EVL-[ARC]EHL) (the theorem)
Step 2: By using substitution, we can say that (ARC)EVL=360°-(ARC)EHL
Thus, when we substitute it back into the theorem, the answer will be <EYL=1/2((360°-(ARC)EHL)-(ARC)EHL)=72°
Step 3: When we solve this out (and you can replace (ARC)EHL with x when solving), you will get an answer of x=108° or (ARC)EHL=108°.
Step 4: (ARC)LVE will be equal to 360°-m(ARC)EHL, which, when we substitute, will be 360°-108°, which will come out to be 252°.
Therefore, by algebra, substitution, and part-whole-postulate, (ARC) LVE=252°.
This is right, this was one of my problems for my 8th grade RSM online homework :)