In a triangle ABC, the measure of angle B is 4 times the measure of angle A, and the measure of angle C is 19 less than 5 times the measure of angle A

Answer 1

The 3 angles of a triangle always add up to 180.

A + B + C = 180 (equation 1)

Because there are 3 variables, we need 3 equations.

B is 4 times greater than A, so:

B = 4*A (equation 2)

Finally, C is 19 less than five times A. This is the trickiest part in my opinion. Let's break it into steps:

C is 19 less than 5*A

We can replace the word "is" with an equal sign.

C = 19 less than 5*A

Now, the equation is almost done!

C = 5*A -19 (equation 3)

We have 3 equations and 3 variables. Now we can start substituting. Let's substitute equation 2 into equation 1.

A + (4*A) + C = 180

Isolate C in equation 3 by subtracting 19 from both sides:

C = 5*A - 19

Substitute equation 3 into equation 1.

A + (4*A) + (5*A - 19) = 180

Let's remove the parentheses (we don't need them!) and combine "like" terms.

10*A - 19 = 180

10*A = 180 + 19 = 199

A = 199/10 = 19.9

Now, we can solve for B and C!

B = 4*A = 4*19.9 = 79.6

C = 5*A + 19 = 5*19.9 + 19 = 80.5