Question
A) 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)
B
B
Answers
GPT 3.5
) The Triangle Angle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees.
Given that the acute angles of the right triangle are 2x + 6 and 3x - 26 degrees, we can set up an equation to find the value of x:
(2x + 6) + (3x - 26) + 90 = 180
5x - 20 + 90 = 180
5x + 70 = 180
5x = 110
x = 22
Now that we have found the value of x, we can substitute 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 missing angles of the right triangle are 50 degrees and 40 degrees.
Given that the acute angles of the right triangle are 2x + 6 and 3x - 26 degrees, we can set up an equation to find the value of x:
(2x + 6) + (3x - 26) + 90 = 180
5x - 20 + 90 = 180
5x + 70 = 180
5x = 110
x = 22
Now that we have found the value of x, we can substitute 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 missing angles of the right triangle are 50 degrees and 40 degrees.