Chapter 7.1, Problem 2PSA

To determine

To calculate: Measure of $\angle 2$ , $\angle 3$ , $\angle 4$ , $\angle 5$ and $\angle 6$

Answer to Problem 2PSA

Measure of $\angle 2$ is $50°$ , $\angle 3$ is $60°$ , $\angle 4$ is $120°$ , $\angle 5$ is $70°$ and $\angle 6$ is $110°$ .

Explanation of Solution

Given information : Here, we have given, $\angle 1=130°$ and $\angle 7=70°$

Formula used : Linear Pair angles are the angles whose sum is $180°$ and Sum of all interior angles of triangle is $180°$ .

Calculation: In the given figure,

  $\angle 1+\angle 2=180°$ (Linear Pair Angles)

  $\begin{array}{l}\Rightarrow 130°+\angle 2=180°\\ \Rightarrow \angle 2=180°-130°\\ \Rightarrow \angle 2=50°\end{array}$

Now, $\angle 7=\angle 5$ (Vertically Opposite Angles)

  $\Rightarrow \angle 5=70°$

Now, $\angle 5+\angle 6=180°$ (Linear Pair Angles)

  $\begin{array}{l}\Rightarrow 70°+\angle 6=180°\\ \Rightarrow \angle 6=180°-70°\\ \Rightarrow \angle 6=110°\end{array}$

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

  $\begin{array}{l}\Rightarrow \angle 5+\angle 3+\angle 2=180°\\ \Rightarrow 70°+\angle 3+50°=180°\\ \Rightarrow 120°+\angle 3=180°\\ \Rightarrow \angle 3=180°-120°\\ \Rightarrow \angle 3=60°\end{array}$

Now, $\angle 3+\angle 4=180°$ (Linear Pair Angles)

  $\begin{array}{l}\Rightarrow 60°+\angle 4=180°\\ \Rightarrow \angle 4=180°-60°\\ \Rightarrow \angle 4=120°\end{array}$