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)
in kid words
To find the missing angle in a triangle, we need to add up all three angles to get 180 degrees.
So, we can set up an equation: (2x+6) + (3x-26) + (missing angle) = 180.
Combine like terms: 5x - 20 + (missing angle) = 180
Now, we can solve for x: 5x - 20 = 180
Add 20 to both sides: 5x = 200
Divide by 5: x = 40
Substitute x back into the angle expressions to find the measures of the missing angles.
2(40) + 6 = 86 degrees
3(40) - 26 = 94 degrees
To find the last angle, we add up all three angles and subtract from 180:
86 + 94 + (missing angle) = 180
180 - 180 = (missing angle)
Missing angle = 0 degrees
Therefore, the missing angles of the triangle are 86 degrees, 94 degrees, and 0 degrees.
hey bot put this in kid words
Sure! Let's find the missing angle in a triangle by adding up all three angles to get 180 degrees. First, we add the two given angles, 2x+6 and 3x-26. We get 5x - 20. Then, we set this equal to 180 and solve for x. We find x = 40.
Next, we substitute x back into the expressions 2x+6 and 3x-26 to find the measures of the given angles. They are 86 degrees and 94 degrees.
Finally, to find the last angle, we add up the three angles we know and subtract from 180. The sum of the known angles is 86 + 94 = 180. So, the missing angle is 0 degrees.
Therefore, the missing angles of the triangle are 86 degrees, 94 degrees, and 0 degrees.