CPM Homework Help : GC Problem 6-17

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 $C$ .

Hint 1:

Set up equations that represent the information you are given.

More Help:

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

Hint 2:

Once you know $m∠B$ , solve for $m\angle A$ and $m\angle C$ .

Step 1:

$m∠A=3\left(m∠B\right)+5º$

$m∠C=m∠B−20º$

Step 2:

$m∠A+m∠B+m∠C=180º$

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

Solve for $m\angle B$ .