Question

A right triangle has acute angles measuring 2x+6 degrees. Use the triangle angle sum theorem to find the measures of the missing anglesof the triangles

Answer 1

I’m missing exactly how the two acute angles are given. Two common interpretations and their solutions:

1) If both acute angles equal 2x + 6 (i.e. the triangle is isosceles):
2(2x + 6) = 90 → 4x + 12 = 90 → 4x = 78 → x = 19.5.
Each acute angle = 2(19.5) + 6 = 45°. So the angles are 45°, 45°, 90°.

2) If the acute angles are 2x + 6 and x:
(2x + 6) + x = 90 → 3x + 6 = 90 → 3x = 84 → x = 28.
Acute angles = 2(28) + 6 = 62° and 28°, so the angles are 62°, 28°, 90°.

If you meant a different setup, tell me the exact expressions for the two acute angles and I’ll solve it.