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Angles and Triangles

Angle measurement, types of triangles, and the angle sum rule.

Measuring Angles

An angle measures the amount of turn between two lines that meet at a point, measured in degrees (°). A full turn is 360 °. A quarter turn (a right angle) is 90 °. A half turn (a straight line) is 180 °.

This course focuses on the right-angled triangle : a triangle with one angle of exactly 90 °. The side opposite the right angle (the longest side) is called the hypotenuse .

Example 1 — finding a missing angle

A triangle has angles of 40 ° and 75 °. Find the third angle. 1 All three angles add to 180 °. 2 Third angle = 180 ° - 40 ° - 75 ° = 65 ° Answer: 65 °

Example 2 — a right-angled triangle

A right-angled triangle has one angle of 35 °. Find the third angle. 1 One angle is 90 ° (the right angle). Another is 35 °. 2 Third angle = 180 ° - 90 ° - 35 ° = 55 ° Answer: 55 °

Practice

A right-angled triangle has one angle of 28 °. What is the third angle, in degrees?

Your answer

Measuring Angles

An angle measures the amount of turn between two lines that meet at a point, measured in degrees (°). A full turn is 360 °. A quarter turn (a right angle) is 90 °. A half turn (a straight line) is 180 °.

Triangles and the Angle Sum Rule

This course focuses on the right-angled triangle : a triangle with one angle of exactly 90 °. The side opposite the right angle (the longest side) is called the hypotenuse .

Example 1 — finding a missing angle

A triangle has angles of 40 ° and 75 °. Find the third angle. 1 All three angles add to 180 °. 2 Third angle = 180 ° - 40 ° - 75 ° = 65 ° Answer: 65 °

Example 2 — a right-angled triangle

A right-angled triangle has one angle of 35 °. Find the third angle. 1 One angle is 90 ° (the right angle). Another is 35 °. 2 Third angle = 180 ° - 90 ° - 35 ° = 55 ° Answer: 55 °

Practice

A right-angled triangle has one angle of 28 °. What is the third angle, in degrees?

Your answer