Angles and angle facts — Mathematics (Grade 10)

Define and explain Angles and angle facts in your own words
Use key terms such as Angle accurately
Apply what you have learned to new examples and questions
Avoid the common mistakes learners make with this topic

Geometry is the mathematics of shape, space and position. From reading a floor plan to programming a robot, its rules let you measure the world and predict what fits where.

This lesson focuses on Angles and angle facts: names of angles, angles on a line and around a point, and angles formed by parallel lines.

Definition: Angles and angle facts

Names of angles, angles on a line and around a point, and angles formed by parallel lines.

Key ideas

Angle facts

Angles on a straight line add to 180 degrees, and angles around a point add to 360 degrees. In a triangle the three interior angles always sum to 180 degrees, so one missing angle can be found by subtracting the other two from 180.

Area formulae

Rectangle: base times height. Triangle: half times base times height, using the perpendicular height, not the slant side. Trapezium: half times the sum of the parallel sides times the distance between them.

Key term — Angle: The amount of turn between two lines that meet, measured in degrees. A right angle is exactly 90 degrees.

Worked example: Angles and angle facts

Two angles on a straight line are 112° and x. Find x.

x = 180 − 112 = 68°.

Answer: x = 180 − 112 = 68°.

Common mistakes

Using the slant height of a triangle as its height The height must be perpendicular to the base; measure straight down to the base line, not along the slanted edge.
Confusing radius and diameter in circle formulae A = πr² uses the radius; C = πd uses the diameter. If given the diameter, halve it first for area.

Practice

Find the perimeter and area of a rectangle 7 cm by 4 cm.

Perimeter adds all sides; area = length × width.

Perimeter = 2(7 + 4) = 22 cm; area = 7 × 4 = 28 cm².

A triangle has base 10 cm and perpendicular height 6 cm. Find its area.

Area = ½ × base × height.

Area = ½ × 10 × 6 = 30 cm².

A trapezium has parallel sides 8 cm and 5 cm, with height 4 cm. Find its area.

Area = ½ × (sum of parallel sides) × height.

Area = ½ × (8 + 5) × 4 = ½ × 13 × 4 = 26 cm².

Find the circumference of a circle with diameter 14 cm (use π = 3.14).

C = πd.

C = 3.14 × 14 = 43.96 cm.

Quick check

Angles and angle facts — quick check

Which of these best defines "Angle"?

The amount of turn between two lines that meet, measured in degrees. A right angle is exactly 90 degrees.

A circle has radius 5 cm. Find its area (use π = 3.14).

A = 3.14 × 25 = 78.5 cm².

Key takeaways

Angles and angle facts: names of angles, angles on a line and around a point, and angles formed by parallel lines.
Angle facts: Angles on a straight line add to 180 degrees, and angles around a point add to 360 degrees.
Parallel: Two lines are parallel when they run in the same direction and never meet, like the rails of a railway track.
Watch out for: using the slant height of a triangle as its height

Triangles and quadrilaterals →Back to Grade 10 chapters Related resources →