Question

A) 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)

Answer 1

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

Since the two given angles are acute angles of a right triangle, one of the angles must be 90 degrees.

Let x be the measure of the missing angle.

So, the sum of the three angles is:
2x + 6 + 3x - 26 + 90 = 180

Combining like terms:
5x + 70 = 180

Subtracting 70 from both sides:
5x = 110

Dividing both sides by 5:
x = 22

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

So, the measures of the missing angles are 40 degrees and 50 degrees.