Answer:
16) B: S = (n - 2)180
17) A: (n - 2)180/n
18) A: 60°
19) ∠e = 50°
20) D: 12°, 133°, 35°
21) D: 37°
Explanation:
16) Generally, formula for finding sum of angles of a convex polygon with n-sides is; S = (n - 2)180
17) the measure of a regular polygon with n sides is; sum of interior angle/number of sides = (n - 2)180/n
18) sum of interior angles is 720.
In the diagram, there are 6 sides of the polygon.
Thus, each interior angle = 720/6 = 120°
Now, sum of angle on a straight line = 180°
Thus;
120 + ∠c = 180
∠c = 180 - 120
∠c = 60°
19) sum of interior angles is 910.
In the diagram, there are 7 sides of the polygon.
Thus, each interior angle = 910/7 = 130°
Now, sum of angles on a straight line = 180°
Thus;
130 + ∠e = 180
∠e = 180 - 130
∠e = 50°
20) sum of angles in a triangle is 180°
Thus, the set that will be correct is the one that has its sum equal to 180°. The only set that falls into this category is;
12°, 133°, 35°
22) Sum of interior angles in a quadrilateral is 360°.
Thus;
3x + 2x + 1 + x + 2 + 4x - 13 = 360
10x - 10 = 360
10x = 360 + 10
x = 370/10
x = 37