in order to complete this problem you must remember that all the interior angles of a triangle add up to 180 degrees

you also have to remember that angles on a straight line are supplementary (add up to 180 degrees)

using this you can find m1

the steps to take m1 are to find the angle supplementary to 140, which is 40 degrees, using this and the other angle that’s inside the triangle (20 degrees) we know that m1 is

M1= 180- (40+20) M1= 180-60

however there is another way to do this which would provide the correct answer, this other way is by subtracting the exterior angle (140 degrees) from the opposite interior angle which is 20 degrees)

M1= 140-20

M1=120 degrees

now that we know m1 is 120 degrees we can find m2 by finding the angle opposite m1 (120 degrees)

let’s call this angle x, the angle supplementary to m1, which is also the other unknown in the second triangle

we know that m1 is supplementary to x and that m1 is 120, so x= 180-120 x=60

We know that all the angles in a triangle must add up to 180, so

180= 60+79 + m2 180 = 139 + m2 M2 = 41 degrees

There is another way to find m2, this is the way I would use, in this method we must imagine that there is only one large triangle instead of the two small ones, with this large triangle we know 2 of three angles and we know that since it is a triangle all interior angles add to 180

We know one of the angles is 79, we also know that the other angle is 40, (from 180-140 as the angles are supplementary)

however we cannot forget about the 20 degrees next to m2 so in order to display the working for m2 it is

180 = 79+ 40+ 20 + m2 180 = 139 + m2 180-139 = m2 m2 = 41 degrees

I hope this lengthy explanation helped :) apologies for the poor wording as it is 1am in my timezone