Chapter 10.1, Problem 8E

To determine

To find the value of x and classify the triangle

Answer to Problem 8E

The value of $x={46}^{\circ }$

The triangle is a scalene triangle

Explanation of Solution

Given information:

One angle of the triangle is ${42}^{\circ }$

Second angle is given as $2x^{\circ }$

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

Calculation:

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

This gives us-

  $2x^{\circ }+x^{\circ }+{42}^{\circ }={180}^{\circ }$

Add both x together

  $3x^{\circ }+{42}^{\circ }={180}^{\circ }$

Subtract 42 from both the sides

  $3x^{\circ }+{42}^{\circ }-{42}^{\circ }={180}^{\circ }-{42}^{\circ }$

This gives us −

  $3x^{\circ }={138}^{\circ }$

Now, divide both sides by 3

  ${\frac{3x}{3}}^{\circ }=\frac{{138}^{\circ }}{3}$

This will give us-

  $x^{\circ }={46}^{\circ }$

Since, the other two angles of the triangle is 2x and x

To find the value of the angle, multiply it with ${46}^{\circ }$

The angle of second side 2x

Multiply 2 with 46

  $2x=2\times {46}^{\circ }$

Which gives us the value as ${92}^{\circ }$

The angle of the third side is x

And the value of $x={20}^{\circ }$

Which gives us the value as ${46}^{\circ }$

Conclusion- The value of $x={46}^{\circ }$

One angle is ${42}^{\circ }$ , Second angle is ${46}^{\circ }$ and the third angle is ${92}^{\circ }$

All the three angles of the triangle are different

Hence, it is scalenetriangle