Question

A hexagon (a six-sided figure) has four angles that have

measures 152°, 108°, 140°, and 172º respectively. The
remaining two angles have the same angle measure.
Explain how to find the two missing angle measures.

Answer 1

74

Explanation:

Sample Response: First find the sum of the interior angles using:180(n – 2). 180(6–2) = 720. Subtract the given angles from 720. 720 – 152 – 108 – 140 – 172 = 148. Since both missing measures are the same, divide 148 by 2. 148 ÷ 2 = 74. So, the remaining angles each measure 74°.

Answer 2

74

Explanation:

A polygon's angles add up to (n-2)*180, where n is the total number of sides, and a hexagon has 6 sides, which means its angles add up to 720 degrees.

Therefore, we can set up an equation where the missing angles, marked as x, and the rest of the angles add up to 720:

x+x+152+108+140+172=720

2x+572=720

2x=148

x=74

Therefore, the angles of the 2 missing angles is 74