Geometric Properties
Discover angle rules for triangles, quadrilaterals and parallel lines — and use them to find unknown angles.
Angles in Triangles
The interior angles of any triangle always add up to 180°. This is one of the most useful rules in geometry.
Equilateral
All angles = 60°
All sides equal
Isosceles
Two equal angles
Two equal sides
Scalene
All angles different
All sides different
Example: Find the missing angle.
A triangle has angles 65° and 80°. Third angle = 180 − 65 − 80 = 35°
Angles in Quadrilaterals
The interior angles of any quadrilateral (four-sided shape) add up to 360°. This is because any quadrilateral can be divided into two triangles (2 × 180° = 360°).
Properties of Common Quadrilaterals
- Square: 4 right angles (90° each)
- Rectangle: 4 right angles (90° each)
- Parallelogram: Opposite angles equal
- Rhombus: Opposite angles equal
- Trapezium: Co-interior angles add to 180°
Finding a Missing Angle
A quadrilateral has angles 85°, 95° and 110°.
Missing angle = 360 − 85 − 95 − 110 = 70°
Angles and Parallel Lines
When a transversal (a line) crosses two parallel lines, special angle pairs are formed. These relationships let us calculate unknown angles.
Corresponding Angles
In the same position at each intersection. They are equal.
Also called "F-angles"
Alternate Angles
On opposite sides of the transversal, between the parallel lines. They are equal.
Also called "Z-angles"
Co-interior Angles
On the same side of the transversal, between the parallel lines. They add to 180°.
Also called "C-angles"
Key Vocabulary
Interior Angle
An angle formed inside a polygon, between two adjacent sides.
Transversal
A line that crosses two or more other lines, creating angle pairs at each intersection.
Parallel Lines
Lines that are always the same distance apart and never meet. Marked with arrows (→→) on diagrams.
Supplementary Angles
Two angles that add up to 180°. They form a straight line when placed together.
Worked Examples
A triangle has angles of 47° and 68°. Find the third angle.
Step 1: Angles in a triangle sum to 180°.
Step 2: Third angle = 180 − 47 − 68 = 65°
A quadrilateral has angles 72°, 108° and 95°. Find the fourth angle.
Step 1: Angles in a quadrilateral sum to 360°.
Step 2: Fourth angle = 360 − 72 − 108 − 95 = 85°
Two parallel lines are cut by a transversal. One co-interior angle is 115°. Find the other.
Step 1: Co-interior angles add to 180°.
Step 2: Other angle = 180 − 115 = 65°
Knowledge Check
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Key Concepts Summary
- ●Angles in a triangle always sum to 180°.
- ●Angles in a quadrilateral always sum to 360°.
- ●Corresponding angles (F-angles) are equal when formed by a transversal crossing parallel lines.
- ●Alternate angles (Z-angles) are equal when formed by a transversal crossing parallel lines.
- ●Co-interior angles (C-angles) add up to 180° when formed by a transversal crossing parallel lines.