Triangles

Diagram of a scalene triangle

For any triangle the 3 angles add up to \(180^\circ\)

Diagram of a scalene triangle with angles of 70°, 50° and an unknown angle marked as x°

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

\[= 180^\circ - 120^\circ = 60^\circ\]

Equilateral triangle

An equilateral triangle is one with all 3 sides equal in length and all 3 angles equal to \(60^\circ\)

Equilateral triangle

Isosceles triangle

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

Diagram of an isosceles triangle with the two equal angles highlighted

Question

In the diagram below the triangle is isosceles. What is the value of \(a^\circ\)?

Isosceles triangle with a 70° base angle and a vertex angle marked as a°

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

\[= 180^\circ - 140^\circ = 40^\circ\]