Chapter 12.2, Problem 4C

To determine

To find:The measures of the numbered angles, 1, 2, 3, 4, 5, 6, 7 in the diagram.

Answer to Problem 4C

The measures of the numbered angles, 1, 2, 3, 4, 5, 6, 7 are $\angle 1={100}^{\circ },\angle 2={100}^{\circ },\angle 3={80}^{\circ },\angle 4={80}^{\circ },\angle 5={100}^{\circ },\angle 6={100}^{\circ },\angle 7={80}^{\circ }$ .

Explanation of Solution

Given:The numbered angles are 1, 2, 3, 4, 5, 6, 7 as given in the diagram.

Calculation: When two lines are crossed by another line then it is known as transversal.

Since, sum of the linear paired angles is ${180}^{\circ }$ .

Therefore,

  ${80}^{\circ }+\angle 1={180}^{\circ }$

  $\begin{array}{l}\Rightarrow \angle 1={180}^{\circ }-{80}^{\circ }\\ \Rightarrow \angle 1={100}^{\circ }\end{array}$

Since, vertically opposite angles are equal.

Therefore,

  $\angle 1\text{ = }\angle 2\text{ and }\angle 3={80}^{\circ }$

  $\Rightarrow \angle 2={100}^{\circ }\text{and }\angle 3={80}^{\circ }$

Since, alternate interior angles are equal.

Therefore,

  $\angle 2=\angle 5={100}^{\circ }\text{ and }\angle 3=\angle 4={80}^{\circ }$

  $\Rightarrow \angle 5={100}^{\circ }\text{ and }\angle 4={80}^{\circ }$

Since, vertically opposite angles are equal.

Therefore,

  $\angle 5=\angle 6={100}^{\circ }\text{ and }\angle 4=\angle 7={80}^{\circ }$

  $\Rightarrow \angle 6={100}^{\circ }\text{ and }\angle 7={80}^{\circ }$

Thus, the measures of the numbered angles, 1, 2, 3, 4, 5, 6, 7 are $\angle 1={100}^{\circ },\angle 2={100}^{\circ },\angle 3={80}^{\circ },\angle 4={80}^{\circ },\angle 5={100}^{\circ },\angle 6={100}^{\circ },\angle 7={80}^{\circ }$ .