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In triangle $ABC$, the angles $\angle A$, $\angle B$, $\angle C$ form an arithmetic sequence. If $\angle A = 45^\circ$, then what is $\angle C$, in degrees?

 Jan 11, 2024

Best Answer 

 #1
avatar+289 
+1

We can write this as an equation, getting:

 

\(45^\circ+45^\circ+x+45^\circ+2x=180^\circ\)

\(135^\circ+3x=180^\circ\)

\(3x=45^\circ\)

\(x=15^\circ\)

 

We can now add \(2x\) to \(45^\circ\) and get:

 

\(30^\circ+45^\circ\)

\(75^\circ\)

 

We get that angle \(C=75^\circ\)

 

Answer: 75°

 Jan 11, 2024
 #1
avatar+289 
+1
Best Answer

We can write this as an equation, getting:

 

\(45^\circ+45^\circ+x+45^\circ+2x=180^\circ\)

\(135^\circ+3x=180^\circ\)

\(3x=45^\circ\)

\(x=15^\circ\)

 

We can now add \(2x\) to \(45^\circ\) and get:

 

\(30^\circ+45^\circ\)

\(75^\circ\)

 

We get that angle \(C=75^\circ\)

 

Answer: 75°

DS2011 Jan 11, 2024

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