Chapter 10.1, Problem 2E

To determine

To find the value of x and classify the triangle

Answer to Problem 2E

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

The triangle is an equilateral triangle

Explanation of Solution

Given information:

One angle of the triangle is ${60}^{\circ }$

The remaining two angles is given as 2x

Calculation:

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

This gives us-

  $2x+2x+{60}^{\circ }={180}^{\circ }$

Add both x together

  $4x+{60}^{\circ }={180}^{\circ }$

Subtract 60 from both the sides

  $4x+{60}^{\circ }-{60}^{\circ }={180}^{\circ }-{60}^{\circ }$

This gives us −

  $4x={120}^{\circ }$

Now, divide both sides by 4

  $\frac{4x}{4}=\frac{{120}^{\circ }}{4}$

This will give us-

  $x={30}^{\circ }$

Since, the other two sides of the triangle is 2x

Multiply it with 2

The angle of each side =

  $x=2\times {30}^{\circ }$

Which gives the value as ${60}^{\circ }$

Hence, all the angles of the triangle is ${60}^{\circ }$

Conclusion- The value of $x={30}^{\circ }$

All the three angles of the triangle is ${60}^{\circ }$

Hence, it is an equilateral triangle