Dear friends, Please read our latest blog post for an important announcement about the website. ❤, The Socratic Team

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

Then teach the underlying concepts
Don't copy without citing sources
preview
?

Explanation

Explain in detail...

Explanation:

I want someone to double check my answer

5
CW Share
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 $\angle A C B = {24}^{\circ}$,
$\implies \angle A B C = 180 - \angle C A B - \angle A C B$
$= 180 - 90 - 24 = {66}^{\circ}$

Then teach the underlying concepts
Don't copy without citing sources
preview
?

Explanation

Explain in detail...

Explanation:

I want someone to double check my answer

2
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..... :)

• 50 minutes ago
• An hour ago
• An hour ago
• An hour ago
• 4 minutes ago
• 7 minutes ago
• 11 minutes ago
• 20 minutes ago
• 26 minutes ago
• 37 minutes ago
• 50 minutes ago
• An hour ago
• An hour ago
• An hour ago
• Che
• Bio
• Cal
• Tri
• Alg
• Sta
• Soc
• Ana
• Wor
• Ast
• Org
• Pre
• Eng
• Phy
• Ast
• Geo
• Psy
• Pre
• U.S
• Ear
• Env