Chapter 10.1, Problem 7E

To determine

To describe and correct the error in finding the value of x

Answer to Problem 7E

The value of x is ${30}^{\circ }$

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

Explanation of Solution

Given information:

One side of the triangle is shown as right angle that is ${90}^{\circ }$

Second side of the triangle is given as $2x^{\circ }$

Third side of the triangle is given as $x^{\circ }$

Calculation:

The sum of all the three sides of the triangle is ${180}^{\circ }$

So, write it as-

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

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

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

Subtract ${90}^{\circ }$ from both the sides

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

In the next step,

  $3x^{\circ }={90}^{\circ }$

Divide both the sides by 3

  $\frac{3x}{3}=\frac{90}{3}$

This will give the value of $x={30}^{\circ }$

Hence the angle measures are

First angle is 2x , multiply 2 with 30

  $x=2\times 30$ , $x={60}^{\circ }$

Second angle x , multiply 1 with 30

  $x=1\times 30$ , $x=30$

Third angle is shown as a right angle which is ${90}^{\circ }$

Hence , write the equation as

  $\begin{array}{l}2x^{\circ }+x^{\circ }+{90}^{\circ }={180}^{\circ }\\ 3x^{\circ }={90}^{\circ }\\ x={30}^{\circ }\end{array}$

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

  $\begin{array}{l}2x^{\circ }+x^{\circ }+{90}^{\circ }={180}^{\circ }\\ 3x^{\circ }={90}^{\circ }\\ x={30}^{\circ }\end{array}$