Question

Find the angle measures of a triangle if the first angle is thirty-one degrees more than the second, and the third is five degrees less than twice the first. Show the equation as well as the complete answer. (Hint: The sum of the interior angles of a triangle is 180 degrees)

Answer 1

Answer:

23°, 54°, 103°

Step-by-step explanation:

let the2nd angle = x

1st angle = x + 31

3rd angle = 2(x + 31) - 5 = 2x + 62 - 5 = 2x + 57

Sum the 3 angles and equate to 180

x + 31 + x + 2x + 57 = 180 , that is

4x + 88 = 180 ( subtract 88 from both sides )

4x = 92 ( divide both sides by 4 )

x = 23

Then

1st angle = x + 31 = 23 + 31 = 54°

2nd angle = x = 23°

3rd angle = 2x + 57 = 2(23) + 57 = 46 + 57 = 103°

Answer 2

Using the triangle sum theorem, the measures of the angles are:

Second angle = 23°

First angle = 54°

Third angle = 103°

What is the Triangle Sum Theorem?

The triangle sum theorem states that the sum of all the interior angles of a triangle equals 180 degrees.

Thus:

Let the second angle be represented as x

Measure of first angle = x + 31

Third angle = 2(x + 31) - 5 = 2x + 62 - 5 = 2x + 57

Thus:

x + x + 31 + 2x + 57 = 180 (triangle sum theorem)

Find x

4x = 180 - 88

4x = 92

x = 23

Plug in the value of x

Second angle = x = 23°

First angle = x + 31 = 23 + 31 = 54°

Third angle = 2x + 57 = 2(23) + 57 = 103°

Learn more about triangle sum theorem on:

https://brainly.com/question/7696843