Applying the properties of shapes to determine an angle

Angles in a triangle add up to 180° and quadrilaterals add up to 360°. Angles can be calculated inside semicircles and circles, as well as with perpendicular bisectors and tangents.

Part of

Maths

Geometric skills

Triangles

This section deals with 2D shapes and angles related to them. It might be worth looking at the National 4 Angles section before continuing.

For any triangle, the three angles add up to $180^\circ$ .

Example

Find the value of $x^\circ$ in the triangle below.

Diagram of a triangle with 70° angle, 50° angle and x° angle

Answer

$x^\circ=180^\circ-(70^\circ+50^\circ)=180^\circ-120^\circ=60^\circ$

An equilateral triangle is one with all three sides equal in length and all three angles equal to $60^\circ$ .

Diagram of an equilateral triangle with three 60° angles

An isosceles triangle is one with two sides equal in length and two equal angles.

Diagram of an isosceles trianglewith two equal angles

Question

In this diagram, the triangle is isosceles so both base angles equal $70^\circ$ .

Diagram of an isosceles triangle with 70° angle and a° angle

What is the value of $a^\circ$ ?

$a^\circ=180^\circ-(70^\circ+70^\circ)=180^\circ-140^\circ=40^\circ$

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Applying the properties of shapes to determine an angle

Triangles

Example

Answer

National 5 Subjects