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Answer:
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