Chapter 10.1, Problem 9E

To determine

To find the value of x and classify the triangle

Answer to Problem 9E

The value of $x={15}^{\circ }$

The triangle is a scalene triangle

Explanation of Solution

Given information:

One angle of the triangle is ${45}^{\circ }$

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

Third angle is given as $5x^{\circ }$

Calculation:

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

This gives us-

  $4x^{\circ }+5x^{\circ }+{45}^{\circ }={180}^{\circ }$

Add both x together

  $9x^{\circ }+{45}^{\circ }={180}^{\circ }$

Subtract 45 from both the sides

  $9x^{\circ }+{45}^{\circ }-{45}^{\circ }={180}^{\circ }-{45}^{\circ }$

This gives us −

  $9x^{\circ }={135}^{\circ }$

Now, divide both sides by 9

  ${\frac{9x}{9}}^{\circ }=\frac{{135}^{\circ }}{9}$

This will give us-

  $x={15}^{\circ }$

Since, the other two sides of the triangle is 4x and 5x

To find the value of the sides multiply it with ${15}^{\circ }$

The angle of second side 4x

Multiply 4 with 15

  $4x=4\times {15}^{\circ }$

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

The angle of the third side is 5x

Multiply 5 with 15

  $5x=5\times {15}^{\circ }$

Which gives us the value as ${75}^{\circ }$

Conclusion- The value of $x={15}^{\circ }$

One side is ${45}^{\circ }$ , Second side is ${60}^{\circ }$ and the third side is ${75}^{\circ }$

Since, all the three sides of the triangle are different

Hence, it is scalene triangle