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.
