Find the measure of each angle below.

Question

In triangle​ ABC, the measure of angle B is

3° more than three times the measure of angle A. The measure of angle C is 42° more than the measure of angle A. Find the measure of each angle.

Answer 1

Good Morning, Dane,

First, as I am certain you know, the total measure of all interior angles in a triangle will equal 180 degrees. If you need some assistance on proving this, I can provide it for you. However, taking that fact at face value, we now know what the sum of the degrees for these angles will be, right? 180 degrees.

Second, we are give all the information we need to solve this problem and what we might want to do now, is assign some algebraic expressions or terms for each of the angles, fair enough? It is clear from the stated problem that < A is not given in the problem, right? So, let's begin there and assign the value of x to that angle, okay? Therefore, the following expressions or terms emerge.

< A = x <---------not given in the problem.

< B = 3x + 3 <---------"the measure of < B is 3 degrees more than three times < A.

< c = x + 42 <---------"The measure of < C is 42 degrees more than the measure of < A.

Remembering that the sum of these three expressions must equal 180 degrees, we now can put together an equation, right?

x + 3x + 3 + x + 42 = 180 <-----Let's combine like terms, okay?

5x + 45 = 180 <-----Let's subtract 45 from both sides of the equation, okay?

5x = 135 <-----Let's solve for x by dividing both sides of the equation by 5, ok?

x = 27 degrees <-----This is the measure of < A

<B = 3x + 3

= 3(27) + 3

= 81 + 3

<B= 84 degrees <-----This is the measure of <B

<C = x + 42

= 27 + 42

<C = 69 degrees <----This is the measure of <C

Now, let's check our work. If our solution to all three measures of <A, <B, and <C are correct, they should add up to 180 degrees, correct?

<A = 27

<B = 84

<C = 69

------------

Sum = 180 degrees.

The solution checks and our answer is valid. As a tutor, I feel it my responsibility to ask: Do you know why the sum of the angles always equal 180?

I hope I have provided you with the assistance you needed tonight, and encourage you to leave any feedback, or questions immediately below in the comment section beneath this answer. If you need further assistance by getting a tutor to work with you one-on-one, please feel free to contact me or any tutor from the many well qualified tutors affiliated with Wyzant. Best!