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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)
To find the measures of the missing angles in the right triangle, we can use the Triangle Angle Sum Theorem, which states that the sum of the angles in any triangle is equal to 180 degrees.
In a right triangle, one angle is always 90 degrees. Let's denote the measure of the right angle as 90 degrees.
Given that the acute angles of the right triangle are 2x+6 and 3x-26 degrees, we can set up an equation to find the values of x:
(2x+6) + (3x-26) + 90 = 180
5x - 20 + 90 = 180
5x + 70 = 180
5x = 110
x = 22
Now that we have found the value of x, we can find the measures of the missing angles:
- The first acute angle: 2(22) + 6 = 50 degrees
- The second acute angle: 3(22) - 26 = 56 degrees
Therefore, the measures of the missing angles in the right triangle are:
- The first acute angle: 50 degrees
- The second acute angle: 56 degrees