can you restate this info The Triangle Angle Sum Theorem states that the sum of the measures of the angles in any triangle is 180 degrees.

Question

can you restate this info The Triangle Angle Sum Theorem states that the sum of the measures of the angles in any triangle is 180 degrees.

In this right triangle, one of the angles is 90 degrees. Therefore, we can set up the equation:

3x + (2x + 10) + 90 = 180

Combining like terms:

5x + 100 = 180

Subtracting 100 from both sides:

5x = 80

Dividing both sides by 5:

x = 16

Substituting x back into the expressions for the angles:

First acute angle: 3x = 3(16) = 48 degrees
Second acute angle: 2x + 10 = 2(16) + 10 = 42 degrees

Therefore, the missing angles of the triangle are 48 degrees and 42 degrees.

Answer 1

The Triangle Angle Sum Theorem states that the total of all the angles in any triangle is always 180 degrees. In this particular triangle, there is a right angle which measures 90 degrees. Consequently, we can create an equation to find the values of the other two angles. By combining like terms, we get the equation 5x + 100 = 180. After subtracting 100 from both sides, we are left with 5x = 80. Dividing both sides by 5, we find that x equals 16. We can then substitute this value back into the expressions for the angles to find that the first acute angle measures 48 degrees, and the second acute angle measures 42 degrees. So, the missing angles in the triangle are 48 degrees and 42 degrees.