Chapter 10: Q.6 (page 539)

The ratio of the angles of a triangle is $6 : 5 : 4$ . Find the angle measures. Then classify the triangle by its angle measures.

Short Answer

Expert verified

The angles measures are $72, 60, 48$ respectively and the triangle is a scalene triangle.

Step by step solution

Step 1. Given Information.

The ratio of angles of a triangle is $6 : 5 : 4$ .

Step 2. Calculation.

Let the angle measures be 6x, 5x, 4x.

The sum of all the angles of a triangle is 180 degree. Hence,

$6 x + 5 x + 4 x = 180 °$

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

$15 x = 180 °$

Divide both the sides by 15.

$\frac{15 x}{15} = \frac{180 °}{15}$

This will give the value of $x = 12$ .

Hence the angle measures are:

First angle is 6x, multiply 6 with 12.

$\begin{array}{l} 6 x = 6 \times 12 \\ = 72 \end{array}$

Second angle 5x, multiply 5 with 12.

$\begin{array}{l} 5 x = 5 \times 12 \\ = 60 \end{array}$

Third angle is 4x, multiply 4 with 12.

$\begin{array}{l} 4 x = 4 \times 12 \\ = 48 \end{array}$

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 $72 {}^{\circ}, 60 {}^{\circ}, 48 °$ and the triangle can be classified as scalene triangle.

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The ratio of the angles of a triangle is $6 : 5 : 4$ . 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 angles of a triangle is6:5:4. 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

Discrete Mathematics

Mechanics Maths

Theoretical and Mathematical Physics

Probability and Statistics

Decision Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

The ratio of the angles of a triangle is $6 : 5 : 4$ . Find the angle measures. Then classify the triangle by its angle measures.