In triangle ABC, angle B is twice as large as angle A. Angle C measures 20° more than angle A. Find the measures of the angles.

Question

I know the angles add up to 180, but im not sure how to set up the rquation to begin solving it. 

Answer 1

let angle A's measurement, in degrees, be a.

Then you are told that angle B's measurement is 2a.

Also, angle C = 2a + 20.

 

Now set the sum of these three measurement expression = 180, and solve the equation.  Please learn from this basic example.

Answer 2

Hi Zoe from Wichita, KS...hope you had a great day at school.

Great question...I will help you set this up for so that you will grasp the concept of these kinds of problems. However, I will not solve it for you...by understanding how to set these problems up and then answer them will make you a pro at knowing how to solve these problems.

Let's begin with what we know...we have a triangle ABC and obviously there are 3 angles inside ABC.

We know that when we add the angle together, it should equal 180°

That means;  m∠A  + m∠B +  m∠C  =   180°       Right?!

Now lets label what your problem gives us:

        m∠A measures something...we'll say:  a  so then  m∠A = a

        m∠B is twice as large as m∠A so then we can write  2 times a = 2a

        m∠C measures 20° more than m∠A so we can write  =  (a  + 20) 

Going back to our equation we confirmed:

                             m∠A + m∠B + m∠C = 180°

Now...let's substitute what we know: 

                               (a) + (2a) + ( a + 20) = 180°

Using the Associative Property of Algebra we re-write:

                              a + 2a + a + 20 = 180°

Re-write         2a + a + a +  20  =  180°     or     4a +  20  =  180°

Now it is your turn to complete the rest and solve for   a.

Make sure you know how to check your answer.