Worked Example 1
Two lines cross. One angle is 68°. Find the other three.
| Angle | Reason | Value |
|---|---|---|
| a | Given | 68° |
| b | a and b make a straight line, so b = 180 - 68 | 112° |
| c | Vertically opposite to a | 68° |
| d | Vertically opposite to b | 112° |
CheckAll four should add to 360, because they go right round a point. 68 + 112 + 68 + 112 = 360. Correct. Doing this check costs five seconds and catches most arithmetic slips.
Worked Example 2
Two parallel lines are cut by a transversal. One angle is 115°. Find all eight.
Think firstThere are only two different sizes in the whole diagram, 115 and its partner on the straight line, which is 180 - 115 = 65. So every one of the eight angles is either 115 or 65. The only work left is deciding which is which.
The quick ruleAngles in the same position at both crossings are equal. Angles next to each other at the same crossing add to 180. Working round the first crossing: 115, 65, 115, 65. Then copy that exact pattern onto the second crossing, because parallel lines slide it along unchanged.
The sentence that earns the marksWrite the reason next to every value, not just the value. For example: co-interior angles are supplementary, so the angle is 180 - 115 = 65. A page of correct numbers with no reasons scores far less than a page with reasons, because the question is testing whether you know why.