Chapter 10.1, Problem 13E

To determine

To find the value of x and classify the triangle

Answer to Problem 13E

The value of $x={63}^{\circ }$

The triangle is a scalene triangle

Explanation of Solution

Given information:

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

Second angle is given as $x^{\circ }+{15}^{\circ }$

Third angle is given as ${39}^{\circ }$

Calculation:

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

This gives us-

  $x^{\circ }+{\left(x+15\right)}^{\circ }+{39}^{\circ }={180}^{\circ }$

Add both numbers and both the x together will give us

  $2x^{\circ }+{54}^{\circ }={180}^{\circ }$

Subtract 54 from both the sides

  $2x^{\circ }+{54}^{\circ }-{54}^{\circ }={180}^{\circ }-{54}^{\circ }$

This gives us −

  $2x^{\circ }={126}^{\circ }$

Now, divide both sides by 2

  ${\frac{2x}{2}}^{\circ }=\frac{{126}^{\circ }}{2}$

This will give us-

  $x={63}^{\circ }$

Since, the first angle of the triangle is given as $x^{\circ }$ and the value of $x={63}^{\circ }$

Second angle of the triangle is $x^{\circ }+{15}^{\circ }$

To find the value of the angle ,add

  ${63}^{\circ }+{15}^{\circ }={78}^{\circ }$

So, the second angle is ${78}^{\circ }$

Conclusion- The value of $x={63}^{\circ }$

So first angle is ${63}^{\circ }$ , Second angle is ${78}^{\circ }$ and the third angle is ${39}^{\circ }$

Since, all the three angles of the triangle are different

Hence, it is scalene triangle