Chapter 7: Q29. (page 244)

Find the measure of each angle.
The measure of the angles of a hexagon are in the ratio $4 : 5 : 5 : 8 : 9 : 9$ .

Short Answer

Expert verified

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

Step by step solution

Step 1. Given Information.

The ratio between angles of a hexagon is,

$4 : 5 : 5 : 8 : 9 : 9$

Step 2. Concept used.

The sum of interior angles of a hexagon is, $720^{\circ}$ .

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,

Step 3. consider the angles as and .

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

$\begin{matrix} 4 x + 5 x + 5 x + 8 x + 9 x + 9 x = 720 \\ 40 x = 720 \\ x = \frac{720}{40} \\ = 18 \end{matrix}$

So, each of the angles are given by,

$\begin{matrix} 4 x = 4 \times 18 \\ = 72 ° \end{matrix}$

$\begin{matrix} 5 x = 5 \times 18 \\ = 90 ° \end{matrix}$

$\begin{matrix} 8 x = 8 \times 18 \\ = 144 ° \end{matrix}$

$\begin{matrix} 9 x = 9 \times 18 \\ = 162 ° \end{matrix}$

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

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Find the measure of each angle.
The measure of the angles of a hexagon are in the ratio $4 : 5 : 5 : 8 : 9 : 9$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Concept used.

Step 3. consider the angles as and .

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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

Step by step solution

Step 1. Given Information.

Step 2. Concept used.

Step 3. consider the angles as and .

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Applied Mathematics

Calculus

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Find the measure of each angle.
The measure of the angles of a hexagon are in the ratio $4 : 5 : 5 : 8 : 9 : 9$ .