Chapter 6.2, Problem 8MRE

To determine

To find: the measures of $\angle 1,\angle 2,\angle 3$ and $\angle 4$ in the given figure.

Answer to Problem 8MRE

The measures of $\angle 1,\angle 2,\angle 3$ and $\angle 4$ is $60°,75°,45°\text{and}\text{60}°$ .

Explanation of Solution

Given information:

Given figure,

Calculation: The angle $\angle 1$ and $\angle 3$ is as follows:

  $\begin{array}{l}\angle 1=60°\\ \angle 3=45°\end{array}$

This is because these are alternate opposite angles of two lines.

Sum of all the angles of the triangles is 180 degrees.

  $\begin{array}{c}60°+45°+\angle 2=180°\\ \angle 2=75°\end{array}$

And, the sum of all the angles on one side of the triangle is 180 degrees.

  $\begin{array}{c}\angle 2+\angle 3+\angle 4=180°\\ 75°+45°+\angle 4=18°\\ \angle 4=60°\end{array}$

Hence, the measures of $\angle 1,\angle 2,\angle 3$ and $\angle 4$ is $60°,75°,45°\text{and}\text{60}°$ .