Question

the angle measures of a triangle are (x+15), (2x-20), and 2x. what are the actual angle measures of the triangle

Answer 1

Hello from MrBillDoesMath!

Answer:

   x + 15 = 52

  2x - 20 = 54

  2x = 74

Discussion:

Let

A = x + 15

B = 2x - 20

C = 2x

A plane triangle has 180 degrees, which in our case, means

A + B + C = 180  or

(x + 15) + (2x-20) + 2x = 180

Combine "x" terms

(x + 2x + 2x) + (15-20) = 180

or

5x -5 = 180

Adding 5 to both sides gives

5x = 185 or x = 37

Therefore

A =  x + 15 = 37 + 15 = 52

B = 2x - 20 = 2(37) - 20 = 74 - 20 = 54

C = 2x  = 2 (37) = 74

Verify that A+B +C = 180   ( 52 + 54 + 74 = 180)

Thank you,

MrB

Answer 2

Using the triangle sum theorem, the actual angle measures of the triangle will be: 52°, 74°, and 54°.

What is the Triangle Sum Theorem?

The theorem states that the sum of all the three interior angles in a triangle will be equal to 180 degrees.

• Therefore:

(x+15) + (2x-20) + 2x = 180

• Solve for x

x + 15 + 2x - 20 + 2x = 180

• Add like terms

5x - 5 = 180

5x = 180 + 5

5x = 185

x = 37

Find the measure of each angles by plugging in the value of x:

x+15 = 37 + 15 = 52°

2x - 20 = 2(37) - 20 = 54°

2x = 2(37) = 74°

Therefore, using the triangle sum theorem, the actual angle measures of the triangle will be: 52°, 74°, and 54°.

Learn more about triangle sum theorem on:

https://brainly.com/question/11120421