Chapter 1, Problem 26RP

To determine

To calculate: Measure of $\angle A$ .

Answer to Problem 26RP

Value of $\angle A$ is $30°$ .

Explanation of Solution

Given information: Here, it is given that $\angle A$ is $6$ greater than twice the measure of $\angle B$ and sum of angles is $42°$ .

Calculation: According to the given information, $\angle A=6+2\angle B$

As, $\angle A+\angle B=42°$ (given)

Putting value of $\angle A=6+2\angle B$ , we get

  $\begin{array}{l}\Rightarrow 6+2\angle B+\angle B=42°\\ \Rightarrow 6+3\angle B=42°\\ \Rightarrow 3\angle B=42°-6\\ \Rightarrow 3\angle B=36°\\ \Rightarrow \angle B=\frac{36°}{3}\\ \Rightarrow \angle B=12°\end{array}$

Now, putting $\angle B=12°$ in $\angle A+\angle B=42°$ , we get

  $\begin{array}{l}\Rightarrow \angle A+12°=42°\\ \Rightarrow \angle A=42°-12°\\ \Rightarrow \angle A=30°\end{array}$