In triangle ABC, the measure of C is twice the measure of A, and the measure of B is 6 times the measure of A. Find the measure of each angle

a + 6a + 2a = 180

a = 20

so now figure B and C

A

B
A
D
All is correct100%

To find the measure of each angle in triangle ABC, let's assume the measure of angle A as x.

We are given that the measure of C is twice the measure of A, so angle C = 2x.
We are also given that the measure of B is 6 times the measure of A, so angle B = 6x.

Keep in mind that the sum of all angles in a triangle is always 180 degrees.

So, the equation for the sum of the angles in triangle ABC would be:
x + 2x + 6x = 180

Combining like terms, we get:
9x = 180

Dividing both sides of the equation by 9, we find:
x = 20

Now, substituting the value of x back into the equations for angles B and C:
Angle B = 6x = 6 * 20 = 120 degrees
Angle C = 2x = 2 * 20 = 40 degrees

Therefore, the measure of angle A is 20 degrees, angle B is 120 degrees, and angle C is 40 degrees.