Question

A right triangle has acute angles measuring degrees and degrees. Use
the Triangle Angle Sum Theorem to find the measures of the missing angles of the
triangle. (4 points)
2x + 6 3x − 26

Answer 1

To find the missing angles of the triangle, we need to use the Triangle Angle Sum Theorem, which states that the sum of all angles in a triangle is equal to 180 degrees.

Let's denote the two acute angles of the right triangle as A and B.

We are given the measures of the two acute angles as 2x + 6 and 3x - 26.

Since the sum of all angles in a triangle is 180 degrees, we can set up the equation:
(2x + 6) + (3x - 26) + 90 = 180

Combining like terms, we have:
5x - 20 + 90 = 180

Simplifying the equation, we get:
5x + 70 = 180

Subtracting 70 from both sides of the equation, we get:
5x = 110

Dividing both sides of the equation by 5, we get:
x = 22

Now that we have the value of x, we can substitute it back into the expressions for the angles to find their measures.

Angle A = 2x + 6 = 2(22) + 6 = 44 + 6 = 50 degrees
Angle B = 3x - 26 = 3(22) - 26 = 66 - 26 = 40 degrees

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