Chapter 10.1, Problem 3E

To determine

To find the value of x and classify the triangle

Answer to Problem 3E

The value of $x={20}^{\circ }$

The triangle is an isoscelestriangle

Explanation of Solution

Given information:

One angle of the triangle is ${80}^{\circ }$

Second angle is given as $4x^{\circ }$

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

Calculation:

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

This gives -

  $4x^{\circ }+x^{\circ }+{80}^{\circ }={180}^{\circ }$

Add both x together

  $5x+{80}^{\circ }={180}^{\circ }$

Subtract 80 from both the sides

  $5x+{80}^{\circ }-{80}^{\circ }={180}^{\circ }-{80}^{\circ }$

This gives us −

  $5x={100}^{\circ }$

Now, divide both sides by 5

  ${\frac{5x}{5}}^{}=\frac{{120}^{\circ }}{5}$

This will give us-

  $x={20}^{\circ }$

Since, the other two angles of the triangle is4x and x

To find the value of the angles multiply it with 20

The angle of second side is4x

Multiply it with 4-

  $4x=4\times {20}^{\circ }$

Which gives the value as ${80}^{\circ }$

The angle of the third side is x

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

Which gives us the value as ${20}^{\circ }$

Conclusion- The value of $x={20}^{\circ }$

One angle is ${80}^{\circ }$ , Second angleis ${80}^{\circ }$ and the third angle is ${20}^{\circ }$

Two sides of the triangle are same and one is different

Hence, it is an isosceles triangle