Question

4. Use the Triangle Angle Sum Theorem to find the largest angle in a triangle with the angle measures of (x + 37)°, (2x + 7)°, and (5x - 8)°.

Answer 1

The Triangle Angle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees.

Therefore, we can set up the equation:

(x + 37) + (2x + 7) + (5x - 8) = 180

Combining like terms:

8x + 36 = 180

Subtracting 36 from both sides:

8x = 144

Dividing by 8:

x = 18

To find the measure of the largest angle in the triangle, substitute x back into the equation:

5x - 8 = 5(18) - 8 = 90 - 8 = 82

Therefore, the largest angle in the triangle is 82 degrees.