Answer:
D) 48°
Explanation:
Step 1: First, we need to know the sum of the measures of the interior angles of the polygon. We can determine the sum using the formula,
(n - 2) * 180, where n is the number of sides of the polygon.
Since this polygon has 4 sides, we plug in 4 for n:
Sum = (4-2) * 180
Sum = 2 * 180
Sum = 360°
Thus, we know that the sum of the measures of the interior angles of the polygon is 360°.
Step 2: Now we can set the sum of four angles equal to 360 to solve for x:
127 + (5x + 3) + 88 + (10x + 7) = 360
215 + (5x + 3 + 10x + 7) = 360
215 + 15x + 10 = 360
225 + 15x = 360
15x = 135
x = 9
Step 3: Now we can plug in 9 for x in the equation representing the measure of E to find the measure of E:
E = 5(9) + 3
E = 45 + 3
E = 48
Thus, the measure of E is 48°
Optional Step 4:
We can check that E = 48 by again making the sum of the angles = 360. We already know the measures of angles J, E, and S so we can just plug in 9 for x in the expression representing angle J. If we get 360 on both sides, we've correctly found the measure of E:
K + J + E + S = 360
(10(9) + 7) + (127 + 48 + 88) = 360
(90 + 7) + 263 = 360
97 + 263 = 360
360 = 360
Thus, we've correctly found the measure of E