SOLUTION: The sum of the measures of three of the interior angles of a convex pentagon is 280. The measure of the fourth angle is three times the measure of the fifth angle. Fin the measur

Question 192078: The sum of the measures of three of the interior angles of a convex pentagon is 280. The measure of the fourth angle is three times the measure of the fifth angle. Fin the measure of the fourth angle.
Answer by orca(409) (Show Source): You can put this solution on YOUR website!
Note that the sum of the measures of the angles of a n-gon is 180(n-2).
So the sum of the measures of the angles of a pentagon is 180(5-2)=540.
As the sum of the measures of the first three angles is 280 degrees, the sum of the measures of the the fourth angle and the fifth angle is 540 - 280 = 260 degrees.

Now let x represent the measure of the fifth angle, then the fourth angle is 3x.
As we have already known their sum is 260, we can set up an equation:
x + 3x = 260
Solving for x, we have:
4x = 260
x = 65
So the 5th angle is 65 degrees
the 4th angle is 3x = 3*65 = 195 degrees.

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