Question

Acellus

x = [?]°
1040
1170
X
124°
1000
Hint: Sum = (n-2)180

Answer 1

Since the sum of the interior angles of a polygon of n sides is (n-2)*180 degrees.

Here n=5 (polygon), so that sum is (5-2)*180 degrees, or 3*180 degrees, or 540 degrees.

Adding up the 5 interior angles shown, we get
Sum = (n-2)*180 =540
100 + 117 + 104 + 124 + x = 540 (degrees).
217 + 228 + x = 540 (degrees).
445 + x =540
Thus, x = 540 - 445 degrees, or x = -4 degrees.

Answer is x = -4

Answer 2

x = 95°

Explanation:

The sum of the interior angles of any polygon is

sum = 180° (n - 2)

Here n = 5, thus

sum = 180° × 3 = 540°

Sum the given angles in the polygon and equate to 540

104° + 117° + 100° + 124° + x = 540°, that is

445° + x = 540° ( subtract 445° from both sides )

x = 95°