Angles on a straight line

J O M and K O N are straight lines. Angle K O L is 62 degrees and angle L O M is 71 degrees. Find angle M O N. First, how an angle's name works. This small one is angle A B C. The middle letter, B, is the corner point, where the two lines meet. The outer two name the lines it sits between. Read it the other way, and angle C B A is the same angle. So ours is angle M O N. K O N is a straight line, so the angles on it add up to one hundred and eighty degrees. Three sit on it: 62 degrees, 71 degrees, and angle M O N. So angle M O N is one hundred and eighty minus 62 minus 71, which is 47 degrees. The bracket says which property gave it. Now angle J O K. You could subtract along J O M. Or see it at once: it faces angle M O N where the lines cross, so they are equal. Both ways give 47 degrees. That is vertically opposite angles.

Your turn. R S T is a straight line. Angle R S U is 43 degrees and angle V S T is 59 degrees. Find angle a. Try it first. Pause if you like. The three angles on line R S T add up to one hundred and eighty degrees. So angle a is one hundred and eighty minus 43 minus 59, which is 78 degrees. And the bracket names the property. One hundred and eighty degrees is the straight line R S T. 43 and 59 are on it, and 78 is what is left. The name says which angle. The bracket says which property.