Chapter 10.1, Problem 20E

To determine

To find the angle measures of the given triangle and classify the triangle

Answer to Problem 20E

The angles measures are $28,64,88$ respectively.

The triangle is a scalene triangle.

Explanation of Solution

Given information:

Ratio of the angle measures in a triangle is given as $7:16:22$

Calculation:

Let the angle measures be 7x, 16x, 22x.

The sum of all the angles of a triangle is 180. Hence,

  $7x+16x+22x={180}^{\circ }$

Adding all the x on the left side of the equation,

  $45x={180}^{\circ }$

Divide both the sides by 45

  $\frac{45x}{45}=\frac{180}{45}$

This will give the value of $x=4$

Hence the angle measures are

First angle is 7x multiply 7 with 4

  $x=7\times 4$ gives $x=28$

Second angle 16x multiply 16 with 4

  $x=16\times 4$ gives $x=64$

Third angle is 22x multiply 22 with 4

  $x=22\times 4$ gives $x=88$

As can be seen all the angle measures are different, which implies that all the sides of the triangle are of different lengths. Hence the triangle is Scalene triangle.

Conclusion- The angle measures of the triangle are $28,64,88$ and the triangle can be classified as Scalene triangle.