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Answer:
Part 1)
Part 2)
Step-by-step explanation:
Part 1) Find the measure of angle CQJ
we know that
The measure of the interior angle is the semi-sum of the arcs comprising it and its opposite.
substitute the values
Part 2) Find the measure of angle LIJ
step 1
Find the measure of angle IJL
we know that
The inscribed angle is half that of the arc it comprises.
substitute the values
step 2
Find the measure of angle ILJ
we know that
The measurement of the external angle is the semi-difference of the arcs it encompasses.
substitute the values
step 3
Find the measure of angle LIJ
Remember that the sum of the interior angles of a triangle must be equal to 180 degrees
In the triangle LIJ
substitute the values