Question

AC←→ is tangent to the circle with center at B. The measure of ∠ACB is 24°. What is the measure of ∠ABC?

Answer 1

`66^@`

Explanation:

Given that `AC` is tangent to the circle and `B` is the center of the circle,
`=> angleCAB=90^@`
Given `angleACB=24^@`,
`=>angleABC=180-angleCAB-angleACB`
`=180-90-24=66^@`

Answer 2

`66^circ`

Explanation:

Now we know that `angleCAB=90^circ` and `angleACB=24^circ`

Our goal is to find the third angle, so we use the property:

`color(brown)("Sum of the three angles of a triangle is"` `color(brown)(180^circ`

So,

`rarrangleCAB+angleACB+angleABC=180^circ`

`rarr90^circ+24^circ+angleABC=180^circ`

`rarr114^circ+angleABC=180^circ`

`rarrangleABC=180^circ-114^circ`

`color(green)(rArrangleABC=66^circ`

Hpe this helps..... :)