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Q.7

Expert-verifiedFound in: Page 539

Book edition
Common Core Edition

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

Pages
183 pages

ISBN
9780547587776

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

The value of *x* is$30\xb0$.

To find the value of *x*, add all the three angles of the triangle that is $2x{}^{\circ}+x{}^{\circ}+90{}^{\circ}=180\xb0$.

One side of the triangle is shown as right angle that is$90\xb0$.

Second side of the triangle is given as$2x\xb0$.

Third side of the triangle is given as$x\xb0$.

**Sum of all angles of a triangle is$180\xb0$.**

The sum of all the angles of a triangle is$180\xb0$.

So, write it as-

$2x{}^{\circ}+x{}^{\circ}+90{}^{\circ}=180\xb0$

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

$3x{}^{\circ}+90{}^{\circ}=180\xb0$

Subtract $90\xb0$ from both the sides.

$3x{}^{\circ}+90{}^{\circ}-90{}^{\circ}=180{}^{\circ}-90\xb0$

In the next step,

$3x{}^{\circ}=90\xb0$

Divide both the sides by 3.

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

This will give the value of $x=30\xb0$

Hence the angle measures are:

First angle is 2*x*, multiply 2 with 30.

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

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$90\xb0$.

Hence, write the equation as,

$\begin{array}{c}2x\xb0+x\xb0+90\xb0=180\xb0\\ 3x\xb0=90\xb0\\ x=30\xb0\end{array}$

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,

$\begin{array}{c}2x\xb0+x\xb0+90\xb0=180\xb0\\ 3x\xb0=90\xb0\\ x=30\xb0\end{array}$

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