Angles — Grade 5 Mathematics
In Grade 5, we classify angles by type and apply key angle rules to find missing angles on straight lines, around a point, and inside triangles.
Types of Angles
AcuteLess than 90°
RightExactly 90°
ObtuseBetween 90° and 180°
StraightExactly 180°
ReflexBetween 180° and 360°
Key Angle Rules
Angles on a straight line add up to 180°.
Angles around a point add up to 360°.
Angles in a triangle add up to 180°.
Vertically opposite angles are equal (formed by two crossing lines).
Special Triangles
- Equilateral triangle: all angles = 60°
- Isosceles triangle: two equal angles (base angles)
- Right-angled triangle: one angle = 90°; the other two sum to 90°
Worked Examples
Example 1 — Angles on a Straight Line
Two angles on a straight line are 47° and x°. Find x.
- Angles on a straight line sum to 180°
- x = 180 − 47 = 133°
Example 2 — Angles in a Triangle
A triangle has angles 65° and 48°. Find the third angle.
- Angles in a triangle = 180°
- Third angle = 180 − 65 − 48 = 67°
Example 3 — Angles Around a Point
Four angles around a point are 90°, 115°, 72°, and a°. Find a.
- All angles around a point = 360°
- a = 360 − 90 − 115 − 72 = 360 − 277 = 83°
Practice Questions
1. An angle on a straight line is 124°. What is the other angle?
✅ 180 − 124 = 56°
2. A triangle has angles 90° and 37°. Find the third angle.
✅ 180 − 90 − 37 = 53°
3. Three angles around a point are 130°, 95°, and 75°. Find the fourth angle.
✅ 360 − 130 − 95 − 75 = 360 − 300 = 60°
4. An isosceles triangle has a top angle of 40°. What are the two base angles?
✅ Remaining = 180 − 40 = 140°; each base angle = 140 ÷ 2 = 70°
5. Two angles on a straight line are (2x + 10)° and (3x − 20)°. Find x and both angles.
✅ (2x + 10) + (3x − 20) = 180 → 5x − 10 = 180 → 5x = 190 → x = 38; angles: 86° and 94°
Key Points to Remember
- Acute < 90°; Right = 90°; Obtuse: 90°–180°; Straight = 180°; Reflex: 180°–360°.
- Straight line rule: angles on one side of a straight line sum to 180°.
- Full turn rule: angles around a point sum to 360°.
- Triangle rule: all three angles inside any triangle sum to 180°.
- To find a missing angle: write the equation, then subtract the known angles from the total.