Find an angle and give the reason
A standard method from Geometry and data basics: the steps and worked examples.
Steps
- Mark every angle you already know on the diagram.
- Find one new angle at a time. After each one, write the reason in brackets.
- Common reasons, in the short form exam markers accept:
| Fact | English short form | 中文 |
|---|---|---|
| Angles on a straight line add to 180° | adj. ∠s on st. line | 直線上的鄰角 |
| Angles at a point add to 360° | ∠s at a pt. | 同頂角 |
| Vertically opposite angles are equal | vert. opp. ∠s | 對頂角 |
| Corresponding angles, parallel lines | corr. ∠s, AB // CD | 同位角，AB // CD |
| Alternate angles, parallel lines | alt. ∠s, AB // CD | 內錯角，AB // CD |
| Interior angles add to 180° | int. ∠s, AB // CD | 同旁內角，AB // CD |
| Angle sum of a triangle | ∠ sum of △ | 三角形內角和 |
| Exterior angle of a triangle | ext. ∠ of △ | 三角形外角 |
| Base angles of an isosceles triangle | base ∠s, isos. △ | 等腰三角形底角 |
Check the short forms against the student's own textbook; publishers differ slightly.
Worked examples
Example 1: Find an angle and give the reason: AB // CD, and a line meets AB at P and CD at Q, with A and D on opposite sides of PQ. ∠APQ = 65°. Find ∠PQD and ∠PQC.
∠PQD = ∠APQ = 65° (alt. ∠s, AB // CD)
∠PQC = 180° − 65° = 115° (adj. ∠s on st. line)For the whole topic, read Geometry and data basics: key points, common mistakes and how the DSE tests it.