The sum of all angles in a triangle is always equal to 180°.
So, we can set up an equation to find the measures of the missing angles:
(2x + 6) + (3x - 26) + missing angle = 180
2x + 6 + 3x - 26 + missing angle = 180
5x - 20 + missing angle = 180
5x + missing angle = 200
missing angle = 200 - 5x
Now, we know that the missing angle must be the right angle of the triangle, so it measures 90°. Therefore, we can write:
200 - 5x = 90
5x = 110
x = 22
Now we can find the measures of the missing angles by substituting x back into the expressions for the cute angles:
2(22) + 6 = 44 + 6 = 50°
3(22) - 26 = 66 - 26 = 40°
Therefore, the measures of the missing angles in the right triangle are 50° and 40°.
A right triangle has a cute angles measuring 2x + 6° and 3x - 26°.
Use the triangle angle sum theorem to find the measures of the missing angles of the triangle.
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