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

Mar 10, 2017

${66}^{\circ}$

#### Explanation:

Given that $A C$ is tangent to the circle and $B$ is the center of the circle,
$\implies \angle C A B = {90}^{\circ}$
Given $\angle A C B = {24}^{\circ}$,
$\implies \angle A B C = 180 - \angle C A B - \angle A C B$
$= 180 - 90 - 24 = {66}^{\circ}$

Mar 11, 2017

${66}^{\circ}$

#### Explanation:

Now we know that $\angle C A B = {90}^{\circ}$ and $\angle A C B = {24}^{\circ}$

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,

$\rightarrow \angle C A B + \angle A C B + \angle A B C = {180}^{\circ}$

$\rightarrow {90}^{\circ} + {24}^{\circ} + \angle A B C = {180}^{\circ}$

$\rightarrow {114}^{\circ} + \angle A B C = {180}^{\circ}$

$\rightarrow \angle A B C = {180}^{\circ} - {114}^{\circ}$

color(green)(rArrangleABC=66^circ

Hpe this helps..... :)