Chapter 12, Problem 8CT

To determine

To find the measures of the other numbered angles in the diagram.

Answer to Problem 8CT

The other numbered angles are obtained as,

  $\begin{array}{l}m\angle 2=52°\\ m\angle 3=52°\\ m\angle 5=128°\\ m\angle 6=52°\\ m\angle 7=52°\\ m\angle 8=128°\end{array}$

Explanation of Solution

Given information:

Thevalue of the angle $m\angle 4$ isgiven as $128°$ .

Concept used:

When a transversal intersects two parallel lines, certain pairs of angles that are formed have equal measures.

Calculation:

Using the concept, the other numbered angles in the diagram can be obtained as,

The angle $m\angle 4\text{ and }m\angle 5$ are alternate interior angles, so the angle $m\angle 5=128°$

The angle $m\angle 5\text{}\text{}\text{ and }m\angle 1$ are corresponding angles, so the angle $m\angle 1=128°$

The angle $m\angle 1\text{ and }m\angle 8$ are alternate exterior angles, so the angle $m\angle 8=128°$

The angle $m\angle 1\text{ and }m\angle 2$ are supplementary angles, so the angle $m\angle 2=52°$

The angle $m\angle 2\text{ and }m\angle 6$ are corresponding angles, so the angle $m\angle 6=52°$

The angle $m\angle 6\text{ and }m\angle 3$ are alternate interior angles, so the angle $m\angle 3=52°$

The angle $m\angle 2\text{ and }m\angle 7$ are alternate exterior angles,so the angle $m\angle 7=52°$

Therefore,

The other numbered angles are obtained as,

  $\begin{array}{l}m\angle 2=52°\\ m\angle 3=52°\\ m\angle 5=128°\\ m\angle 6=52°\\ m\angle 7=52°\\ m\angle 8=128°\end{array}$