Chapter 4, Problem 10CUR

To determine

Find the measure of each numbered angle.

Answer to Problem 10CUR

  $m\angle 1=75°$

  $m\angle 2=40°$

  $m\angle 3=40°$

  $m\angle 4=65°$

Explanation of Solution

Given:

  

Calculation:

The diagram is :

  

Since $AB\parallel CD$

  $m\angle 4=m\angle C=65°$ , since they are corresponding angles , where AC is the transversal and AB is parallel to CD.

  $\begin{array}{l}m\angle 3+m\angle AED=180°\mathrm{................}[\text{linear angles]}\\ \Rightarrow m\angle 3+140°=180°\\ \Rightarrow m\angle 3=180°-140°\mathrm{.................}[\text{subtract 140}°\text{ from each side]}\\ \Rightarrow m\angle 3=40°\end{array}$

  $m\angle 2=m\angle 3=40°$ , since they are alternate inerior angles , where AE is the transversal and AB is parallel to CD.

  $\begin{array}{l}m\angle 1+m\angle 3+m\angle C=180°\\ \Rightarrow m\angle 1+40°+65°=180°\\ \Rightarrow m\angle 1+105°=180°\\ \Rightarrow m\angle 1=180°-105°\mathrm{.................}[\text{subtract 105}°\text{ from each side]}\\ \Rightarrow m\angle 1=75°\end{array}$

So,

  $m\angle 1=75°$

  $m\angle 2=40°$

  $m\angle 3=40°$

  $m\angle 4=65°$