Question

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

Answer 1

When two tangent lines intersect, they form an angle that equals
one half (larger intercepted arc minus the smaller intercepted arc)

So, angle CLA = (1/2) (200 -160)
Angle CLA = (1/2) (40)
Angle CLA = 20 degrees

Source:
http://www.1728.org/circangl.htm

Answer 2

Answer:

The correct option is D.

Step-by-step 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.

$\text{Included angle}=\frac{1}{2}(\text{Major arc - Minor arc})$

According to the given figure,

$\angle CLA=\frac{1}{2}(Arc(AKC)-Arc(AC))$

$\angle CLA=\frac{1}{2}(200^{\circ}-160^{\circ})$

$\angle CLA=\frac{1}{2}(40^{\circ})$

$\angle CLA=20^{\circ}$

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