Chapter 11.2, Problem 83HP

To determine

Find the measurement of the largest angle.

Answer to Problem 83HP

The largest angle is ${84}^0$ . Option B is correct.

Explanation of Solution

Given:

The measures of the angle of a triangle form an arithmetic sequence. If the measure of the smallest angle is ${36}^0$ , what is the measure of the largest angle?

4 options are:

  

Concept Used:

We know that sum of three angles of a Triangle is ${180}^0$

According to the question, the measures of the angle of a triangle form an arithmetic sequence .

Let the angles are: $a^0,{(a+d)}^0,{(a+2d)}^0$

Smallest angle is $a^0$ and the largest angle is ${(a+2d)}^0$

Calculation:

Given: The smallest angle $a^0={36}^0$

Sum of three angles of a Triangle is ${180}^0$

  $\begin{array}{l}a+a+d+a+2d=180\\ 3a+3d=180\\ 3·36+3d=180\\ 108+3d=180\\ 108-108+3d=180-108\\ 3d=72\\ \frac{3d}{3}=\frac{72}{3}\\ d=24\end{array}$

  $\begin{array}{l}\text{The}\text{largest}\text{angle}=a+2d\\ a+2d=36+2·24=36+48={84}^0\end{array}$

Thus, the largest angle is ${84}^0$ . Option B is correct.