High School

The measure of angle F is 62 degrees, and angle H is 87 degrees in triangle FGH. What is the value of x in the expression (3x + 2) degrees?

Answer :

Final answer:

To find the value of x, subtract the given angles from 180° to find the third angle. Then solve the equation (3x + 2)° = 31° to get x ≈ 9.67 degrees.

Explanation:

To find the value of x in triangle FGH where the measure of angle F is 62 degrees and angle H is 87 degrees, you start by knowing that the sum of the interior angles in a triangle is always 180 degrees. With the given measures, the third angle, G, can be calculated as:

180° - 62° - 87° = 31°

Since the measure of angle G is given by the expression (3x + 2) degrees, we can set up the equation:

(3x + 2)° = 31°

Solving for x, we get:

3x = 31° - 2°

3x = 29°

x = 29° / 3

x = 9.67 degrees (approximately)

Thus, x is approximately 9.67 degrees.