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Triangles Unit Test

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Question
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)

1 answer

To find the measures of the missing angles, we first need to recognize that the sum of the angles in any triangle is always 180 degrees.

Given that the acute angles of the right triangle are 2x+6 and 3x-26 degrees, we can set up an equation:

(2x+6) + (3x-26) + 90 = 180
5x - 20 + 90 = 180
5x + 70 = 180
5x = 110
x = 22

Now we can substitute x back into the expressions for the acute angles to find their measures:

2(22) + 6 = 50 degrees
3(22) - 26 = 40 degrees

So, the missing acute angles of the right triangle are 50 degrees and 40 degrees.
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