Chapter 6, Problem 3CR

To determine

To Find: The measure of larger angle when information about supplementary angles is given

Answer to Problem 3CR

Measure of the larger angle=$131°$

Explanation of Solution

Given information:

We are given that the measure of larger angle is $16$ less than the thrice of its supplement.

Concept Used: Solving linear equations in one variable

Calculation:

As per the question we have two supplementary angles.

Let say the larger angle =

  $x$

Thus, the smaller angle = $180°\text{ - }x$ .

Applying the given condition on these two angles we can write as:

  $\begin{array}{l}x=3(180°-x)-16\\ \Rightarrow x=540°-3x-16\\ \Rightarrow x+3x=524°\\ \Rightarrow 4x=524°\\ \Rightarrow x=\frac{524°}{4}\\ \Rightarrow x=131°\end{array}$

Conclusion:

Measure of the larger angle=$131°$