Chapter 7: Q31. (page 244)

The measures of the consecutive angles of a quadrilateral are in the ratio $5 : 7 : 11 : 13$ . Find the measure of each angle.

Short Answer

Expert verified

The measure of each angle is $50^{\circ}, 70^{\circ}, 110^{\circ}$ and $130^{\circ}$ .

Step by step solution

Step 1. Given information.

The ratio of the consecutive angles of a quadrilateral are,

$5 : 7 : 11 : 13$

Step 2. Concept used.

The sum of angles of a quadrilateral is $360^{\circ}$

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

it might not represent the actual measure.

So,

Step 3. Considering the angles as5x,7x,11x,13x.

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

$\begin{matrix} 5 x + 7 x + 11 x + 13 x = 360 \\ 36 x = 360 \\ x = 10 \end{matrix}$

So each of the angles are given by,

$\begin{matrix} 5 x = 5 \times 10 \\ = 50 \\ 7 x = 7 \times 10 \\ = 70 \\ 11 x = 11 \times 10 \\ = 110 \\ 13 x = 13 \times 10 \\ = 130 \end{matrix}$

Therefore, the measure of each angle of quadrilateral is $50^{\circ}, 70^{\circ}, 110^{\circ}$ and $130^{\circ}$ .

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The measures of the consecutive angles of a quadrilateral are in the ratio $5 : 7 : 11 : 13$ . Find the measure of each angle.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. Considering the angles as5x,7x,11x,13x.

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The measures of the consecutive angles of a quadrilateral are in the ratio5:7:11:13 . Find the measure of each angle.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. Considering the angles as5x,7x,11x,13x.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Probability and Statistics

Theoretical and Mathematical Physics

Statistics

Calculus

Study anywhere. Anytime. Across all devices.

The measures of the consecutive angles of a quadrilateral are in the ratio $5 : 7 : 11 : 13$ . Find the measure of each angle.