Question

The figure below shows a triangle with vertices A and B on a circle and vertex C outside it. Side AC is tangent to the circle. Side BC is a secant intersecting the circle at point X:

The figure shows a circle with points A and B on it and point C outside it. Side BC of triangle ABC intersects the circle at point X. A tangent to the circle at point A is drawn from point C. Arc AB measures 152 degrees, and angle CBA measures 64 degrees.

What is the measure of angle ACB?

32°
6°
24°
12°

Answer 1

is there a image?

Answer 2

Right?

Answer 3

@kekeman

Answer 4

@kekeman

Answer 5

Here is the image: https://snipboard.io/0a8nQL.jpg

Answer 6

e.e i havnt done this stuff in a yr

Answer 7

Ooop

Answer 8

@az

Answer 9

Okay

Answer 10

First things first, you need to calculate the length of arc AX

Answer 11

the angle XBA = 1/2 * arc AX

and we know angle XBA is 64

the arc is just going to be twice of that

so what would arc AX be?

Answer 12

and then to measure angle ACB, you need to use this

so angle ACB = 1/2 (arc AB - arc AX)

so you know arc AB is 152
and you just calculated arc AX right before this

so now you can calculate angle ACB

Answer 13

So the answer would be 12° right?

Answer 14

arc AX is 128

so angle ACB = 1/2 * (152 - 128)
= 1/2 * (24)
= 12