Chapter 7: Q26. (page 244)

Find the measure of each angle.
The measures of the angles of a triangle are in the ratio $3 : 4 : 5$ .

Short Answer

Expert verified

The measure of each angle is $45^{\circ}, 60^{\circ}$ and $75^{\circ}$ .

Step by step solution

Step 1. Given information.

The ratio between angles of a triangle is,

$3 : 4 : 5$

Step 2. Concept used.

The sum of angles of a triangle is $180^{\circ}$

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

it might not represent the actual measure.

Step 3. Consider the angles as3x,4x, and5x .

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

$\begin{matrix} 3 x + 4 x + 5 x = 180 \\ 12 x = 180 \\ x = 15 \end{matrix}$

So each of the angles are given by,

$\begin{matrix} 3 x = 3 \times 15 \\ 3 x = 45 \\ 4 x = 4 \times 15 \\ 4 x = 60 \end{matrix}$

And,

$\begin{matrix} 5 x = 5 \times 15 \\ 5 x = 75 \end{matrix}$

Therefore, the measure of each angle is $45^{\circ}, 60^{\circ}$ and $75^{\circ}$ .

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Find the measure of each angle.
The measures of the angles of a triangle are in the ratio $3 : 4 : 5$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. Consider the angles as3x,4x, and5x .

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Find the measure of each angle.The measures of the angles of a triangle are in the ratio3:4:5.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. Consider the angles as3x,4x, and5x .

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Mechanics Maths

Statistics

Logic and Functions

Geometry

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Find the measure of each angle.
The measures of the angles of a triangle are in the ratio $3 : 4 : 5$ .