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.