Question

For three angles A, B, and C, the measure of Bis twice the measure of A, the measure of C is three times the measure of A, and the sum of the angle measures is 180. What is the measure of each angle?

Answer 1

Answer: A=30 degrees, B=60 degrees, C=90 degrees

Explanation:

B=2A

C=3A

A+B+C=180

A+2A+3A=180

6A=180

A=30 degrees

B=2A

B=2(30)

B=60 degrees

C=3(30)

C=90 degrees

Answer 2

Angle A = 30°

Angle B = 60°

Angle C = 90°

Explanation:

Let x represent the measure of A. Using this information, we can figure out the measure of B and C in terms of x.

Since B is twice the measure of A, then it would be 2x. Similarly, C is three times the measure of A, thus it would b 3x.

We also know that the sum of the angles is 180 degrees. We can use this information to set up an equation.

Setting up an Equation

We know that:

Angle A + Angle B + Angle C = 180

Substituting the values we gave for A, B, and C, we find:

x + 2x + 3x = 180

Now, we solve the equation for x.

Solving the Equation

Start by combining like terms:

6x = 180

Now, divide both sides by 6:

x = 30

Since we know the value of x, we can find the values of the angles.

Finding the Values of Each Angle

A = x = 30°

B = 2x = 60°

C = 3x = 90°