Question

A right triangle has acute angles measuring 2x+6 degrees and 3x−26 degrees. Use the Triangle Angle Sum Theorem to find the measures of the missing angles of the triangle

Answer 1

pls make it smaller

Answer 2

thanks

Answer 3

The sum of the angles in a triangle is always 180 degrees.

So, we can set up an equation:

(2x+6) + (3x-26) + (90) = 180

Combine like terms:

5x - 20 + 90 = 180

5x + 70 = 180

Subtract 70 from both sides:

5x = 110

Divide by 5:

x = 22

Now we can find the measures of the missing angles:

2x+6 = 2(22) + 6 = 44 + 6 = 50 degrees

3x-26 = 3(22) - 26 = 66 - 26 = 40 degrees

Therefore, the missing angles of the triangle are 50 degrees and 40 degrees.

Answer 4

Sure, here is a more concise explanation:

Given angles: 2x+6, 3x-26

Using the Triangle Angle Sum Theorem: (2x+6) + (3x-26) + 90 = 180

Solving for x:
5x - 20 + 90 = 180
5x + 70 = 180
5x = 110
x = 22

Find the missing angles:
2x+6 = 2(22) + 6 = 50 degrees
3x-26 = 3(22) - 26 = 40 degrees

Therefore, the missing angles of the triangle are 50 degrees and 40 degrees.

Answer 5

You're welcome! If you have any more questions, feel free to ask.