The Triangle Angle Sum Theorem states 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 write the equation:
(2x+6) + (3x-26) + 90 = 180
Simplifying the equation:
5x - 20 + 90 = 180
5x + 70 = 180
5x = 110
x = 22
Now, we can substitute the value of x back into the expressions for the acute angles:
2x+6 = 2(22)+6 = 50 degrees
3x-26 = 3(22)-26 = 40 degrees
Therefore, the missing angles of the triangle are:
90 degrees (right angle)
50 degrees
40 degrees
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)
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