To find the measures of the missing angles of the right triangle, we first need to recall the Triangle Angle Sum Theorem. This theorem states that the sum of the interior angles of a triangle is always 180 degrees.
In the right triangle given, we are given two of the angles: 2x+6 degrees and 3x-26 degrees. Since it is a right triangle, one of the angles is 90 degrees.
Therefore, the sum of the three angles in the triangle would be:
(2x+6) + (3x-26) + 90 = 180
Combining like terms, we get:
5x - 20 + 90 = 180
5x + 70 = 180
Subtracting 70 from both sides:
5x = 110
Dividing by 5:
x = 22
Now, we can find the measures of the missing angles by substituting the value of x back into the expressions for the angles:
Angle 1: 2(22) + 6 = 50 degrees
Angle 2: 3(22) - 26 = 40 degrees
So, the three angles of the right triangle are:
Angle 1: 50 degrees
Angle 2: 40 degrees
Angle 3: 90 degrees
The Triangle Angle Sum Theorem helped us find the measures of the missing angles by applying the concept that the sum of the interior angles of a triangle is always 180 degrees.
make it long but not too long please explain it too
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.
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