What is the measure of arc AB when m angle APB = 78.

Solution:

Given, the measure of angle APB = 78°

We have to find the measure of arc AB.

From the given figure,

We observe that it's the type of angle whose vertex is outside the circle and its sides intersect the circle.

By using the tangent-tangent angle formula,

m∠APB = (1/2)(ALB - AB)

m∠APB = angle of the vertex

ALB = measure of arc ALB

AB = measure of arc AB

We know that the total measure of an arc is equal to 360 degrees.

So, ALB + AB = 360°

Let the measure of arc AB be x.

ALB + x = 360°

ALB = 360° - x

Substitute the value of APB and ALB in the formula,

78° = (1/2)[(360° - x) - x]

156° = 360° - 2x

2x = 360° - 156°

2x = 204°

x = 204/2

x = 102°

Therefore, the measure of arc AB is 102°.

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What is the measure of arc AB when m angle APB = 78.

Summary:

The measure of arc AB when m angle APB = 78° is 102°.