Quick Concept Summary
Geometry aptitude usually rewards a clean diagram more than heavy calculation. Mark given values, write the standard angle facts, and solve only what is needed.
Core Facts
| Shape | Key fact |
|---|---|
| Triangle | Interior angles total 180 degrees |
| Quadrilateral | Interior angles total 360 degrees |
| Straight line | Angles total 180 degrees |
| Circle | Radius is perpendicular to tangent at contact point |
Worked Examples
Example 1
A triangle has angles 45 degrees and 65 degrees.
Third angle = 180 - 45 - 65 = 70 degrees
Example 2
The exterior angle of a triangle is 120 degrees; one remote interior angle is 50 degrees.
Other remote interior angle = 120 - 50 = 70 degrees
Practice Questions
1. Find the fourth angle of a quadrilateral if the others are 80, 95, and 110 degrees. 2. A circle has radius 7 cm. Find circumference using pi = 22/7. 3. Two supplementary angles are in ratio 2:3. Find them.
Common Mistakes
- Mixing radius and diameter
- Forgetting that a straight line gives 180 degrees
- Assuming a diagram is to scale