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

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 \(180^\circ\).

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

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

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

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

- Question
In this diagram, the triangle is isosceles so both base angles equal \(70^\circ\).

What is the value of \(a^\circ\)?

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