Based on the given angles of the pentagon, the measure of angle A is 73 degrees.
How to find the measure of angle A
To find the measure of angle A, use the properties of angles in a pentagon.
A pentagon has five angles, and the sum of the interior angles in any pentagon is given by the formula:
Sum of interior angles = (n - 2) * 180 degrees
where n is the number of sides of the polygon (in this case, n = 5 for a pentagon).
Substitute n = 5 into the formula, we have:
Sum of interior angles = (5 - 2) * 180 degrees
Sum of interior angles = 3 * 180 degrees
Sum of interior angles = 540 degrees
To find the measure of angle A, represent the fifth interior angle as x
First, find the value of x
we can subtract the sum of the other four angles from the sum of the interior angles:
x = Sum of interior angles - (96 + 115 + 118 + 104)
x = 540 - (96 + 115 + 118 + 104)
x = 540 - 433
x = 107 degrees
Now to find the measures of A, Since exterior angle A is supplementary to x, we have
A = 180 - 107
A = 73 degree
Therefore, the measure of angle A is 73 degrees.