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Chapter 7: Q29. (page 244)

Find the measure of each angle.

The measure of the angles of a hexagon are in the ratio4:5:5:8:9:9 .

Short Answer

Expert verified

The measure of each angle of the hexagon is, 72掳,90掳,90掳,144掳,162掳,162掳.

Step by step solution

01

Step 1. Given Information.

The ratio between angles of a hexagon is,

4:5:5:8:9:9

02

Step 2. Concept used.

The sum of interior angles of a hexagon is, 720鈭�.

A hexagon has six sides and six interior angles.

Since, ratio of the angles is always in the simplified form,

it might not represent the actual measure. So,

03

Step 3. consider the angles as and .

The sum of the angles of the hexagon can be expressed using the above relation as,

4x+5x+5x+8x+9x+9x=72040x=720x=72040=18

So, each of the angles are given by,

4x=4脳18=72掳

5x=5脳18=90掳

8x=8脳18=144掳

9x=9脳18=162掳

Therefore, the angles of the hexagon are.72掳,90掳,90掳,144掳,162掳,162掳

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