Answer:
[tex]m \angle 6 = 90^\circ[/tex]
Step-by-step explanation:
We are given the following in the question:
[tex]l \parallel m\\\angle 1 = 140^\circ\\\angle 3 = 50^\circ[/tex]
We have to find the measure of [tex]\angle 6[/tex].
Angle 1 and angle 2 forms a pair of straight angle. That is the sum of measure of both angle is equal to 180 degrees. Thus, we can write:
[tex]\angle 1 + \angle 2 = 180^\circ\\\text{Putting the measure of angle 1}\\140 + \angle 2 = 180\\\angle 2 = 180-140\\\angle 2 = 40^\circ[/tex]
Now, [tex]\angle 1, \angle 2, \angle 6[/tex] forms the three angles of the triangle.
Now, by angle sum property of triangle the sum of all the three angle of the triangle is 180 degrees.
Thus, we can write:
[tex]\angle 2 + \angle 3 + \angle 6 = 180^\circ\\\text{Putting the values}\\40 + 50 + \angle 6 = 180\\\angle 6 = 180 - 40-50\\\angle 6 = 90^\circ[/tex]
Measure of angle 6 is 90 degrees.
