Chapter 1, Problem 7RP

To determine

The measure of the given $\angle \text{A}$ i.e., $m\angle A$

Answer to Problem 7RP

The measure of the given $\angle \text{A}$ is $\text{20}°$ ,i.e., $m\angle A=\text{20}°$

Explanation of Solution

Given information:

  $\angle A\cong \angle B$ and $\angle A=\left(2x+5\right)°and\angle B=\left(50-4x\right)°$

Formula used: Congruency means same size and same shape

Calculation:

Since, $\angle A\cong \angle B$ , then

  $\angle A=\angle B$.......(i) (By definition of congruency)

Put the values of $\angle A\text{ and }\angle \text{B}$ in (i) as given, $\angle A=\left(2x+5\right)°$ and $\angle B=\left(50-4x\right)°$

  $\begin{array}{l}2x+5=50-4x\\ \Rightarrow 2x+4x=50-5\\ \Rightarrow 6x=45\\ \Rightarrow x=\frac{45}{6}=7.5\\ \text{Hence,}\\ m\angle A=2\times 7.5+15+5=20°\end{array}$