In triangle FGH, the measure of angle G is three times that of angle F. The measure of angle H is 20 degrees more that that of angle F. Find the angle measures
F + 3F + F + 20 = 180
5F = 160
F = ?
To solve this problem, let's denote the measure of angle F as x degrees.
According to the given information:
- The measure of angle G is three times that of angle F, so angle G = 3x degrees.
- The measure of angle H is 20 degrees more than that of angle F, so angle H = x + 20 degrees.
The sum of the angles in a triangle is always 180 degrees. Therefore, we can write the equation:
Angle F + Angle G + Angle H = 180
Substituting the values we found earlier, we have:
x + 3x + (x + 20) = 180
Combine like terms:
5x + 20 = 180
Subtract 20 from both sides:
5x = 160
Divide both sides by 5:
x = 32
Now we can substitute this value of x back into the expressions for angle G and angle H to find their measures:
Angle G = 3x = 3 * 32 = 96 degrees
Angle H = x + 20 = 32 + 20 = 52 degrees
Therefore, the measure of angle F is 32 degrees, angle G is 96 degrees, and angle H is 52 degrees in triangle FGH.