Question

Situation #1

The ratio of the interior angles of a hexagon is 5:5:6:7:8:9.
1a. What is the measurement of the 10 points
second-largest interior angle in this
hexagon?
Your answer:
1b. What is the measurement of the 10 points
interior angle that appears twice in
this hexagon?
Your answer:

Answer 1

a) 144°

b) 90°

Explanation:

You want the measures of the 2nd largest, and the smallest, of the angles in a hexagon whose ratios are 5:5:6:7:8:9.

Hexagon

The interior angles of a hexagon will have a sum of ...

180°×(n -2) = 180°×(6 -2) = 720°

Ratio

The sum of the numbers in the given ratio is ...

5+5+6+7+8+9 = 40

This tells us that multiplying the ratio values by 720/40 = 18 will give the angle values:

90:90:108:126:144:162

Second largest

The second largest angle is 144°.

Repeated

The smallest angle, 90°, is the one that is repeated.