Chapter 10: Q.20 (page 540)

The ratio of the angle of a triangle is $7 : 16 : 22$ . Find the angle measures. Then classify the triangle by its angle measures.

Short Answer

Expert verified

The angles measures are $28 {}^{\circ}, 64 {}^{\circ}, 88 °$ respectively and the triangle is a scalene triangle.

Step by step solution

Step 1. Given Information.

The ratio of angles of a triangle is $7 : 16 : 22$ .

Step 2. Calculation.

Let the angle measures be 7x, 16x, 22x.

Sum of all angles of a triangle is $180 °$ .Hence,

$7 x + 16 x + 22 x = 180 °$

Add all the x on the left side of the equation.

$45 x = 180 °$

Divide both the sides by 45.

$\frac{45 x}{45} = \frac{180 °}{45}$

This will give the value of $x = 4$ .

Hence the angle measures are:

First angle is 7x, multiply 7 with 4.

$\begin{matrix} 7 x = 7 \times 4 \\ = 28 \end{matrix}$

Second angle 16x, multiply 16 with 4.

$\begin{matrix} 16 x = 16 \times 4 \\ = 64 \end{matrix}$

Third angle is 22x, multiply 22 with 4.

$\begin{matrix} 22 x = 22 \times 4 \\ = 88 \end{matrix}$

As all the angle measures are different, which implies that all the sides of the triangle are of different lengths. Hence the triangle is scalene triangle.

Step 3. Conclusion.

The angle measures of the triangle are and the triangle can be classified as scalene triangle.

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The ratio of the angle of a triangle is $7 : 16 : 22$ . Find the angle measures. Then classify the triangle by its angle measures.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

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The ratio of the angle of a triangle is7:16:22. Find the angle measures. Then classify the triangle by its angle measures.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Pure Maths

Probability and Statistics

Mechanics Maths

Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.

The ratio of the angle of a triangle is $7 : 16 : 22$ . Find the angle measures. Then classify the triangle by its angle measures.