To find the measures of the missing angles of the triangle, we first need to recall the Triangle Angle Sum Theorem, which states that the sum of the interior angles of a triangle is always 180 degrees. In this case, we have a right triangle, which means that one of the angles is a right angle measuring 90 degrees.
Let's denote the measures of the acute angles as 2x+6 and 3x-26 degrees. Since the sum of all three angles is 180 degrees, we can set up an equation:
(2x+6) + (3x-26) + 90 = 180
Simplifying, we get:
5x - 20 + 90 = 180
5x + 70 = 180
5x = 110
x = 22
Now that we have found the value of x, we can plug it back into the expressions for the acute angles to find their measures:
2(22) + 6 = 50 degrees
3(22) - 26 = 40 degrees
Therefore, the measures of the missing angles of the right triangle are 50 degrees and 40 degrees.
make it long but not too long please
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.
1 answer