Question

What is the measure of arc AB when m angle APB=78
102
156
204
39

Answer 1

Answer: 102

Explanation:

m∠APB = (ALB - AB) m∠APB = angle of the vertex ALB = measure of arc ALB AB = measure of arc AB we all know that the total measure of arc is equal to 360,
hence, ALB + AB = 360 let: x = measure of arc AB 360 - x = measure of arc ALB substitute: 78 = {(360 - x) - x} 78 = (360 - 2x) 78 = 180 - x.
Simplifying further by dividing both 360 and -2x by 2 x = 180 - 78 combining like terms x = 102

Arc AB = 102 = Answer

Answer 2

In the given figure above, we can use the formula for tangent-tangent angle. This is under the type of angle whose vertex is outside the circle and its sides intersects the circle.

Applying 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 all know that the total measure of arc is equal to 360, hence, ALB + AB = 360

let: x = measure of arc AB
360 - x = measure of arc ALB

substitute:

78 =
`(1)/(2)` {(360 - x) - x}
78 =
`(1)/(2)` (360 - 2x)
78 = 180 - x ⇒ simplifying further by dividing both 360 and -2x by 2
x = 180 - 78 ⇒ combining like terms
x = 102
arc AB = 102 ⇒ Answer