Chapter 7.1, Problem 1PSA

To determine

To calculate: Measure of $\angle B$

Answer to Problem 1PSA

Measure of $\angle B$ is $70°$ .

Explanation of Solution

Given information : Here, we have given, a triangle in which $\angle A$ is $40°$ and $\overline{AB}=\overline{AC}$ .

Formula used : Sum of all interior angles of triangle is $180°$ .

Calculation: As, $\overline{AB}=\overline{AC}$ ,

  $\Rightarrow \angle B=\angle C$ (Angles opposite to equal side of a triangle are equal)

Let $\angle B=x$ ,

  $\Rightarrow \angle C=x$

Now, as sum of all interior angles of a triangle is $180°$ .

  $\begin{array}{l}\Rightarrow \angle A+\angle B+\angle C=180°\\ \Rightarrow 40°+x+x=180°\\ \Rightarrow 40°+2x=180°\\ \Rightarrow 2x=180°-40°\\ \Rightarrow 2x=140°\\ \Rightarrow x=\frac{140°}{2}\\ \Rightarrow x=70°\end{array}$

  $\therefore \angle B=x=70°$