Chapter 11.5, Problem 30CCR

To determine

Tocalculate : Themeasure of the angle.

Answer to Problem 30CCR

  $\angle 1=85°$ , $\angle 2=50°$ and $\angle 3=45°$

Explanation of Solution

Given information : The given angles are $\angle 4=95°$ and $\angle 5=135°$

  

Formula used : We know the sum of the supplementary angle is $180°$ . And the sum of the interior angle of the triangle is $180°$ .

Calculation : Use the sum of supplementary angle to find $\angle 1$ and $\angle 3$

  $\begin{array}{l}\angle 1+\angle 4=180°\\ \angle 1+95°=180°\\ \angle 1=180°-95°\\ \angle 1=85°\end{array}$

Also,

  $\begin{array}{l}\angle 5+\angle 3=180°\\ \angle 3+135°=180°\\ \angle 3=180°-135°\\ \angle 3=45°\end{array}$

Now, the sum of the interior angle of the triangle is $180°$ .

  $\begin{array}{l}\angle 1+\angle 2+\angle 3=180°\\ 85°+\angle 2+45°=180°\\ \angle 2+130°=180°\\ \angle 2=180°-130°\\ \angle 2=50°\end{array}$