Question

Measure of angle LOI= 38 degrees

Measure of angle JOP= 84 degrees
Find measure of angle JKP

Answer 1

The measure of angle JKP is 61°

Explanation:

we know that

If the measure of angle m<LOI=38°

then

m arc IL=38° -----> by central angle

and

If the measure of angle m<JOP=84°

then

m arc JP=84° -----> by central angle

Remember that

The measure of the interior angle is the semi-sum of the arcs that comprise it and its opposite.

so

m<JKP=(1/2)[arc IL+arc JP]

substitute the values

m<JKP=(1/2)[38°+84°]=61°