Chapter 11, Problem 13SGR

To determine

To find the value of $m\angle 1$ .

Answer to Problem 13SGR

  $m\angle 1=68°$

Explanation of Solution

Given information:

There are two parallel lines, ‘m’ and ‘n’, that is cut by a transversal ‘r’ and $m\angle 4=112°$ .

Formula used:

Supplementary angles, to calculate the measure of angles.

Calculation:

The figure given in the questions consists of two parallel lines, ‘m’ and ‘n’ that is cut by a transversal ‘r’. In this case, it is observed that $m\angle 4$ and $m\angle 1$ lie on the same line, adjacent to each other. Since there are no other angles around them, they are supplementary in nature. In means, that $m\angle 4$ and $m\angle 1$ add up to $180°$ .

  $m\angle 1+m\angle 4=180°$

As discussed above.

  $=>m\angle 1+112°=180°$

Putting the value of $m\angle 4$ in the equation.

  $=>m\angle 1=180°-112°$

Calculating the value.

  $=>m\angle 1=68°$

Hence this is the vale.