Question

Calculate the m angle CLA , given m arc AC = 160° and m arc AKC = 200°.

answer options:
A. 90˚
B. 180˚
C. 40˚
D. 20˚

Answer 1

The correct option is D.

Explanation:

Given information: Measure of arc AC = 160° and arc AKC = 200°.

If two tangents intersecting outside the circle then their included angles is equal to half of difference of major and minor arc.

According to the given figure,

`\angle CLA=(1)/(2)(Arc(AKC)-Arc(AC))`

`\angle CLA=(1)/(2)(200^(\circ)-160^(\circ))`

`\angle CLA=(1)/(2)(40^(\circ))`

`\angle CLA=20^(\circ)`

The measure of angle CLA is 20°. Therefore the correct option is D.