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

The Triangle Angle Sum Theorem states that the sum of the angles in a triangle is always equal to 180 degrees.

In this case, we are given two acute angles of the right triangle: 2x+6 and 3x-26 degrees.

The third angle of the triangle can be found by subtracting the sum of the two given angles from 180 degrees:

180 - (2x+6 + 3x-26) = 180 - 5x - 20
180 - 5x - 20 = 160 - 5x

The third angle of the triangle is equal to 160 - 5x degrees.

Since it is a right triangle, one of the angles is 90 degrees. Therefore, the sum of the three angles is equal to 180 degrees:

90 + (2x+6) + (3x-26) = 180
90 + 2x + 6 + 3x - 26 = 180
5x + 70 = 180
5x = 110
x = 22

Now we can find the measures of the missing angles:

- The third angle is 160 - 5(22) = 50 degrees.
- The angles of the right triangle are 90 degrees, 2(22)+6 = 50 degrees, and 3(22)-26 = 40 degrees.