A right triangle has acute angles measuring 2x + 6° and 3x - 26° using the triangle angle sum theorem to measure to find the measures of the missing angles of the triangle

Answer 1

Let's use the triangle angle sum theorem to find the measures of the missing angles.

In a triangle, the sum of all three angles is 180°.

So, we have:

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

Simplify the equation:

5x - 20 + ? = 180

Add 20 to both sides:

5x + ? = 200

Since the triangle is a right triangle, one of the angles is 90°.

Now we can substitute this information back into our equation:

5x + 90 = 200

Subtract 90 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°
3x - 26 = 3(22) - 26 = 66 - 26 = 40°

Therefore, the measures of the missing angles are:
50°, 40°, and 90°.