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Q.7

Expert-verified

Pre-algebra

Found in: Page 539

Book edition Common Core Edition

Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff

Pages 183 pages

ISBN 9780547587776

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Short Answer

Describe and correct the error in finding the value of x for the triangle shown below.

The value of x is $30 °$ .

To find the value of x, add all the three angles of the triangle that is $2 x {}^{\circ}+ x {}^{\circ}+ 90 {}^{\circ}= 180 °$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

One side of the triangle is shown as right angle that is $90 °$ .

Second side of the triangle is given as $2 x °$ .

Third side of the triangle is given as $x °$ .

Step 2. Formula.

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

Step 3. Calculation.

The sum of all the angles of a triangle is $180 °$ .

So, write it as-

$2 x {}^{\circ}+ x {}^{\circ}+ 90 {}^{\circ}= 180 °$

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

$3 x {}^{\circ}+ 90 {}^{\circ}= 180 °$

Subtract $90 °$ from both the sides.

$3 x {}^{\circ}+ 90 {}^{\circ}- 90 {}^{\circ}= 180 {}^{\circ}- 90 °$

In the next step,

$3 x {}^{\circ}= 90 °$

Divide both the sides by 3.

$\frac{3 x}{3} = \frac{90}{3}$

This will give the value of $x = 30 °$

Hence the angle measures are:

First angle is 2x, multiply 2 with 30.

$\begin{array}{l} 2 x = 2 \times 30 \\ = 60 \end{array}$

Second angle x, multiply 1 with 30.

$\begin{array}{l} x = 1 \times 30 \\ = 30 \end{array}$

Third angle is shown as a right angle which is $90 °$ .

Hence, write the equation as,

$\begin{matrix} 2 x ° + x ° + 90 ° = 180 ° \\ 3 x ° = 90 ° \\ x = 30 ° \end{matrix}$

Step 4. Conclusion.

Since all the three sides of the triangle are given, add all the sides and not just two sides.

Hence, the correct equation in finding the value of x is,

$\begin{matrix} 2 x ° + x ° + 90 ° = 180 ° \\ 3 x ° = 90 ° \\ x = 30 ° \end{matrix}$

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