Four lines meet at a ponit. find the measures of angle m and angle n.

Okay so this won't be the easiest for me to explain by typing but i'll do my best

this is a geometry question. a couple important things to know are as follows:

1) all of the quadrants should add up to ninety because two of the lines crossing eachother have a 90 degree square.

2) every angle diagonal from another one are the same. so if two lines cross in an X shape, the top angle and the bottom angle are equal and the two side angles are equal.

so now we're ready to start.

let's start with angle N. it will be easiest.

using the rule of the diagonals, you'll notice that N is diagonal to the 90° square therefore it too is 90°

N = 90°

next, angle M. using the diagonal rule, the angle across from the 15° is going to also be 15°, that means that that quadrant has an angle of 40° and 15°. now recall that all the quadrants must add up to 90°. so from this we can make a simple equation:

40° angle + 15° angle + M angle = 90°

now solve for M angle

40 + 15 + M = 90    55 + M = 90    M = 35°

so N = 90° and M = 35°