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.(4 points) WRITE IT SHORT AND ONLY FIND THE MEASURES AND WRITE IT LIKE A 7TH GRADER

Answer 1

In a triangle, the angles add up to 180 degrees. Since it's a right triangle, one angle is 90 degrees, and the other two angles are 2x + 6 and 3x - 26 degrees.

Let's set up the equation:

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

Now, combine like terms:

2x + 6 + 3x - 26 + 90 = 180
5x + 70 = 180

Next, subtract 70 from both sides:

5x = 110

Now, divide by 5:

x = 22

Now, plug x back into the angle expressions:

1. For the first angle:
2(22) + 6 = 44 + 6 = 50 degrees

2. For the second angle:
3(22) - 26 = 66 - 26 = 40 degrees

So, the measures of the angles are:

- First angle: 50 degrees
- Second angle: 40 degrees
- Right angle: 90 degrees

The triangle has angles measuring 50°, 40°, and 90°.