Question

problem 19:
(first taught in
lesson 30)
find m + n.
after you enter your answer press go.
m + n =

Explanation:

Step1: Use the property of parallel lines and alternate - interior angles

Since the two lines are parallel, we know that \(m = 40\) (alternate - interior angles).

Step2: Use the property of a straight line

The sum of angles around a point on a straight line formed by the transversal and the parallel lines. We know that \(m + n=180 - 40\) (linear - pair related to the \(40^{\circ}\) angle). But more simply, using the property of the angles between parallel lines and a transversal.
Another way:
Let's consider the fact that if we extend the lines and use the angle - chasing. The sum of \(m\) and \(n\) and the \(40^{\circ}\) angle (using the property of parallel lines and the angles formed by a transversal). The sum of \(m\) and \(n\) is \(140\).
We can also use the formula for the sum of angles formed by two parallel lines and a transversal. If we assume the transversal cuts the two parallel lines, and we know that the non - adjacent angles (in the case of the angles inside the "Z" - like shape formed by the transversal and parallel lines)
Let's use the fact that the sum of the angles \(m\) and \(n\) and the \(40^{\circ}\) angle (if we consider the full - turn around the intersection point of the transversal and the right - hand parallel line, but since the lines are parallel, we can use the property that \(m + n=180 - 40\) (because of the supplementary angles formed with the \(40^{\circ}\) angle and the angles \(m\) and \(n\) in the non - overlapping part of the transversal - parallel line intersection)

Answer:

\(140\)