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Given Arc KM measures 130 degrees, what is the measure of angle MLK?

Given Arc KM measures 130 degrees, what is the measure of angle MLK?-example-1

2 Answers

7 votes

Final answer:

The measure of angle MLK is equal to 130 degrees if MLK is a central angle with point L at the center. If MLK is an inscribed angle, it's 65 degrees, half the measure of the intercepted arc KM.

Step-by-step explanation:

To determine the measure of angle MLK given that Arc KM measures 130 degrees, we must first understand the relationship between the measure of an arc and the central angle that intercepts that arc in a circle. In a circle, the measure of a central angle is equal to the measure of the arc it intercepts.

Assuming that point L is the center of the circle, and KM is an arc of the circle intercepted by angle MLK, the measure of angle MLK would be equal to the measure of arc KM. Since arc KM is given as 130 degrees, the measure of angle MLK is also 130 degrees.

If point L is not at the center and instead MLK is an inscribed angle, then MLK would measure half the degree measure of the intercepted arc, which in this case would be 65 degrees (half of 130).

User JasonMichael
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6 votes

Answer:

m<MLK = 65°

Step-by-step explanation:

Measure of intercepted arc KM = 130°

<MLK is the inscribed angle of the intercepted arc.

Therefore, measure of inscribed angle = ½ the measure of its intercepted arc.

Thus:

m<MLK = ½(130)

m<MLK = 65°

User Rojj
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