Question

In a triangle, the measure of the first angle is twice the measure of the second angle. The measure of the third angle is 8° less that the measure of the second angle. What is the measure of each angle? Solve using the fact that the sum of the measures of the three angles of a triangle is 180°. Show and check your work.​

Answer 1

1st angle = 94°

2nd angle = 47°

3rd angle = 39°

Explanation:

Let 2x be the first angle, let x be the second angle, and let x-8 be the third angle.

The sum of the measures of the angles of a triangle add to 180°, so the equation would be (2x)+(x)+(x-8)=180

First, combine like terms - 4x-8=180

Next, add 8 to both sides - 4x=188

Then, to get x by itself, divide both sides by 4 - x=47

Finally, plug in 47 to find the measures of each angle:

2(47)=94° - 1st angle, 47° - 2nd angle, 47-8=39°

All three angle measures should add to 180°

Answer 2

Answer:the measure of the first angle is 94 degrees

the measure of the second angle is 47 degrees

Let z represent the measure of the third angle is 39 degrees

Explanation:

Let x represent the measure of the first angle.

Let y represent the measure of the second angle.

Let z represent the measure of the third angle.

The measure of the first angle is twice the measure of the second angle. This means that

x = 2y

The measure of the third angle is 8° less that the measure of the second angle. This means that

z = y - 8

that the sum of the measures of the three angles of a triangle is 180°. This means that

x + y + z = 180 - - - - - - - - -1

Substituting x = 2y and z = y - 8 into equation 1, it becomes

2y + y + y - 8 = 180

4y = 180 + 8 = 188

y = 188/4 = 47

x = 2y = 2 × 47 = 94 degrees

z = y - 8 = 47 - 8 = 39 degrees.