Chapter 10.1, Problem 6E

To determine

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

Answer to Problem 6E

The angles measures are $72,60,48$ respectively.

The triangle is a scalene triangle.

Explanation of Solution

Given information:

Ratio of the angle measures in a triangle is given as $6:5:4$

Calculation:

Let the angle measures be 6x, 5x, 4x.

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

  $6x+5x+4x={180}^{\circ }$

Adding all the x on the left side of the equation

  $15x={180}^{\circ }$

Divide both the sides by 15

  $\frac{15x}{15}=\frac{180}{15}$

This will give the value of $x=12$

Hence the angle measures are

First angle is 6xmultiply 6 with 12

  $x=6\times 12$ get $x=72$

Second angle 5x multiply 5 with 12

  $x=5\times 12$ get $x=60$

Third angle is 4x multiply 4 with 12

  $x=4\times 12$ get $x=48$

As 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 72, 60 and 48 and the triangle can be classified as Scalene triangle.