Question

A right triangle has acute angles measuring 2x+6 degrees and 3x-26 degrees. Use the triangle sum theorem to find the measures of the missing angles of triangle. (4 points)

Answer 1

The triangle sum theorem states that the sum of the angles in any triangle is 180 degrees.

Thus, we have:

(2x+6) + (3x-26) + (missing angle) = 180

Combining like terms, we get:

5x - 20 + (missing angle) = 180

Adding 20 to both sides:

5x + (missing angle) = 200

Subtracting 5x from both sides:

(missing angle) = 200 - 5x

To find the measures of the missing angles, we need to know the value of x. Without additional information, we cannot determine the specific measures of the missing angles.

Answer 2

wrong

Answer 3

I apologize for the incorrect response. Let's solve the equation correctly.

According to the triangle sum theorem, the sum of the angles in any triangle is 180 degrees.

So we have:

(2x+6) + (3x-26) + (missing angle) = 180

Combining like terms, we get:

5x - 20 + (missing angle) = 180

Adding 20 to both sides:

5x + (missing angle) = 200

Subtracting 5x from both sides:

(missing angle) = 200 - 5x

Since the missing angle is opposite to the hypotenuse, it must be the right angle, which measures 90 degrees.

Therefore, we have:

90 = 200 - 5x

Subtracting 200 from both sides:

-110 = -5x

Dividing by -5:

x = 22

Now we can substitute x back into the expressions for the acute angles to find their measures:

2x + 6 = 2(22) + 6 = 44 + 6 = 50 degrees

3x - 26 = 3(22) - 26 = 66 - 26 = 40 degrees

So, the measures of the missing angles are 50 degrees and 40 degrees.