Chapter 10.1, Problem 12E

To determine

To find the value of x and classify the triangle

Answer to Problem 12E

The value of $x={33}^{\circ }$

The triangle is a scalene right-angled triangle

Explanation of Solution

Given information:

First angle of the triangle is given as $2x^{\circ }$

Second angle is given as $x^{\circ }$

Third angle is given as ${\left(3x-18\right)}^{\circ }$

Calculation:

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

This gives us-

  $2x^{\circ }+x^{\circ }+{\left(3x-18\right)}^{\circ }={180}^{\circ }$

Add both the x together, this

will give us

  $3x^{\circ }+{\left(3x-18\right)}^{\circ }={180}^{\circ }$

Again add both the x and add 18 on both the sides

  $6x^{\circ }-{18}^{\circ }+{18}^{\circ }={180}^{\circ }+{18}^{\circ }$

This gives us −

  $6x^{\circ }={198}^{\circ }$

Now, divide both sides by 6

  ${\frac{6x}{6}}^{\circ }=\frac{{198}^{\circ }}{6}$

This will give us-

  $x={33}^{\circ }$

Since, the first angle of the triangle is given as $2x^{\circ }$

To find the value of the angle ,multiply 2 with 33

  $2\times 33={66}^{\circ }$

So, the first angle is ${66}^{\circ }$

The second angle of the triangle is given as x and the value of $x={33}^{\circ }$

The third angle of the triangle is given as ${\left(3x-18\right)}^{\circ }$

To find out the value of x ,multiply 3 times 33 and the subtract 18 from it-

  $3\times 33-18={81}^{\circ }$

So, the third angle of the triangle is ${81}^{\circ }$

Conclusion- The value of $x={33}^{\circ }$

First angle measurement is ${66}^{\circ }$ , Second angle is ${33}^{\circ }$ and the third angle is ${81}^{\circ }$

Since, all the three angles of the triangle are different

Hence, it is scalene right-angled triangle