I'm needing help with understanding /solving this problem. Can you please help? In triangle ABC, the angle C is six times as large as angle A. The measure of angle B is 20 degree greater that that of angle A. Find the measure of the angles.
A + A - 20 + 6A = 180
8A = 200
A = 25
Sure, I'd be happy to help you understand and solve this problem!
To find the measures of the angles in triangle ABC, we need to set up and solve a system of equations based on the given information.
Let's call the measure of angle A as "x" degrees.
From the problem statement, we know that angle C is six times as large as angle A. So, the measure of angle C is 6x degrees.
We are also given that angle B is 20 degrees greater than angle A. So, the measure of angle B is x + 20 degrees.
Now, we can use these equations to solve for the values of x, angle A, angle B, and angle C.
The sum of the angles in any triangle is always 180 degrees. So, the equation formed by the sum of the angles in triangle ABC is:
A + B + C = 180
Substituting the values we found earlier, we get:
x + (x + 20) + 6x = 180
Simplifying the equation, we have:
8x + 20 = 180
Now, we can solve for x:
8x = 180 - 20
8x = 160
x = 160/8
x = 20
Now that we have the value of x, we can find the measures of angle A, angle B, and angle C.
Angle A = x = 20 degrees
Angle B = x + 20 = 20 + 20 = 40 degrees
Angle C = 6x = 6 * 20 = 120 degrees
So, the measures of the angles in triangle ABC are: Angle A = 20 degrees, Angle B = 40 degrees, and Angle C = 120 degrees.