### Home > CCG > Chapter 6 > Lesson 6.1.4 > Problem6-38

6-38.

Solve the problem below using any method. Show all work.

Angle $A$ of $ΔABC$ measures $5º$ more than $3$ times the measure of angle $B$. Angle $C$ measures $20º$ less than angle $B$. Find the measure of angles $A$, $B$, and $C$.

Set up equations that represent the information you are given.

What is the sum of the angles within a triangle?
How can you use this to find $∠B$?

One you know $m∠B$, solve for angles $A$ and $C$.

$m∠A=3m∠B+5º$

$m∠C=m∠B−20º$

$m∠A+m∠B+m∠C=180º$

Substitute.
$(3m∠B+5º)+m∠B+(m∠B−20º)=180º$

Solve for $B$.