Worked Example 1
Three angles of a quadrilateral are 85°, 100° and 65°. Find the fourth.
ReasoningA diagonal splits any quadrilateral into two triangles, so the four angles add to 2 × 180 = 360°.
Working85 + 100 + 65 = 250. Fourth angle = 360 - 250 = 110°.
Check85 + 100 + 65 + 110 = 360. Correct. Notice you were never told what kind of quadrilateral it was, and you never needed to know.
Worked Example 2
One angle of a parallelogram is 70°. Find the other three.
| Angle | Reason | Value |
|---|---|---|
| A | Given | 70° |
| B | Neighbouring angles are co-interior on parallel sides, so they add to 180 | 110° |
| C | Opposite to A, and opposite angles of a parallelogram are equal | 70° |
| D | Opposite to B | 110° |
The reason is the answerEvery value in the middle column traces back to Unit 1: co-interior angles are supplementary, alternate angles are equal. A student who writes only 110, 70, 110 has done the arithmetic but not the question.