Question

For #1 and #2, use the figure on the right. L.K and LM are tangent to the circle. Both KJ and MJ connect to the center of the circle at point J.

1. What is the measurement of angle KJM

2. What is the measurement of angle LMJ ?

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Answer 1

Measure of angle KJM: 60 degrees

Measure of angle LMJ: 120 degrees

1. Measuring Angle KJM

Since angle L is 60 degrees, arc JL must measure 120 degrees (twice the angle at the center).

In a circle, the sum of the angles subtended by an arc is equal to the measure of the arc. Therefore, angle KJM measures:

120 degrees / 2 = 60 degrees

Therefore, the revised measure of angle KJM is 60 degrees.2. Measuring Angle LMJ

Since angle LMJ is adjacent to angle KJM and they are on a straight line, they are supplementary angles and add up to 180 degrees. Thus, angle LMJ measures:

180 degrees - 60 degrees = 120 degrees

Therefore, the revised measure of angle LMJ is 120 degrees.