The measure of <B is 20 less than <A. The measure of <C is twice <A. Find the measure of each angle. Classify by angles.

Answer 1

Let's start by turning your problem statement into a system of equations.

First, we know that the sum of the angles in a triangle must equal 180 degrees. Therefore, we can write: A+B+C=180

Second, we know that angle B is 20 degrees less than angle C. This can be written as: B=A-20

Third, we know that angle C is two times bigger than angle A. This means: C=2A

We can solve this system of equations, as we have 3 equations and 3 unknowns.

1. A+B+C=180
2. B=A-20
3. C=2A

We can substitute equations (2) and (3) into equation (1) to get: A+A-20+2A=180 ---> 4A-20=180. This means that A=50 degrees.

We can then plug A=50 back into equations (2) and (3) to find that B=30 degrees and C=100 degrees.