Chapter 11, Problem 4STP

To determine

To find the angle measure that is not one of the angles of the triangle.

Answer to Problem 4STP

J. $118°$

Explanation of Solution

Given information:

Measures of the interior angles are given in the ratio $5:6:19$ .

Formula used:

Sum of the interior angles of a triangle add up to $=180°$

Calculation:

To calculate the measures of the interior angles that are provided in a ratio, convert the three ratios by multiplying each with a constant ‘x’.

This will give $5:6:19$

  $=5x,6x,19x$

Once the constant is multiplied, their sums would add up to $=180°$ .

or, $5x+6x+19x=180°$

upon simplifying,

  $=>30x=180°$

Bringing the numeric values in the right-hand side.

  $=>x=\frac{180°}{30}$

Dividing the numerator by the denominator.

  $=>x=6°$

This is the value of the constant ‘x’.

Upon multiplying this with the original parts of the ratio, the measure of the three angles of the triangle would be obtained.

First angle is $5x=5\times 6°$

  $=30°$

Second angle is $6x=6\times 6°$

  $=36°$

Third angle is $19x=19\times 6°$

  $=114°$

Upon looking at the options, angle in option J is not present.

Hence this is the angle not part of the triangle.