Chapter 12, Problem 11MCQ

To determine

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

Answer to Problem 11MCQ

The measure of the numbered angles are,

  $m\angle 1=68°,m\angle 2=112°,m\angle 3=112°,m\angle 4=68°,m\angle 5=68°,m\angle 7=112°$and $m\angle 8=68°$

Explanation of Solution

Given information: If $m\angle 6$

  $={112}^{\circ }$ , find the measures of the other numbered angles in the diagram.

  

Calculation:

The angles, $m\angle 5$ and $m\angle 6$ are supplementary angle.

Therefore, $m\angle 5+m\angle 6=180°$

Or, $m\angle 5=180°-m\angle 6$

  $\begin{array}{l}=180°-112°\\ =68°\end{array}$

When a line crosses two other lines it’s called transversal, the angles which are on the matching corners, are the corresponding angles. The corresponding angles are equal when those two straight lines are parallel.

So, $m\angle 1=m\angle 5=68°$ [ $\angle 1$ and $\angle 5$ are corresponding angles], and $m\angle 2=m\angle 6=112°$ [ $\angle 2$ and $\angle 6$ are corresponding angles], and $m\angle 1$ and $m\angle 3$ are supplementary angles.

Therefore, $m\angle 1+m\angle 3=180°$

Or, $m\angle 3=180°-m\angle 1$

  $\begin{array}{l}=180°-68°\\ =112°\end{array}$

  $m\angle 2$ and $m\angle 4$ are supplementary angles

Therefore, $m\angle 2+m\angle 4=180°$

Or, $m\angle 4=180°-m\angle 2$

  $\begin{array}{l}=180°-112°\\ =68°\end{array}$

  $m\angle 5$ and $m\angle 7$ are supplementary angles

Therefore, $m\angle 5+m\angle 7=180°$

Or, $m\angle 7=180°-m\angle 5$

  $\begin{array}{l}=180°-68°\\ =112°\end{array}$

  $m\angle 6$ and $m\angle 8$ are supplementary angles

Therefore, $m\angle 8+m\angle 6=180°$

Or, $m\angle 8=180°-m\angle 6$

  $\begin{array}{l}=180°-112°\\ =68°\end{array}$

Hence, The measure of the numbered angles are,

  $m\angle 1=68°,m\angle 2=112°,m\angle 3=112°,m\angle 4=68°,m\angle 5=68°,m\angle 7=112°$and $m\angle 8=68°$