Triangle angles total 180. A line through a vertex parallel to the opposite side transfers the other two angles to that vertex; together they form a straight angle. An exterior angle equals the sum of the two non-adjacent interior angles. **Triangle** | **Useful property** Isosceles | Two equal sides have equal opposite angles; two equal angles have equal opposite sides. Equilateral | Three equal sides; three angles of 60. Scalene | All three sides differ. Right-angled | One angle is 90; the other two total 90. Example In an isosceles triangle, the angle between the equal sides is 44. Each base angle is 180 -44 2=68. An exterior angle at a base vertex is 112 =44 +68. “Acute”, “right-angled” and “obtuse” classify triangles by their angles. Side-based and angle-based descriptions can both apply to the same triangle.

Triangle angles total \(180^\circ\). A line through a vertex parallel to the opposite side transfers the other two angles to that vertex; together they form a straight angle. An exterior angle equals the sum of the two non-adjacent interior angles.

In an isosceles triangle, the angle between the equal sides is \(44^\circ\). Each base angle is \(\dfrac{180^\circ-44^\circ}{2}=68^\circ\). An exterior angle at a base vertex is \(112^\circ=44^\circ+68^\circ\).

“Acute”, “right-angled” and “obtuse” classify triangles by their angles. Side-based and angle-based descriptions can both apply to the same triangle.

Triangles and their angles

Triangles and their angles

Triangle	Useful property
Isosceles	Two equal sides have equal opposite angles; two equal angles have equal opposite sides.
Equilateral	Three equal sides; three angles of \(60^\circ\).
Scalene	All three sides differ.
Right-angled	One angle is \(90^\circ\); the other two total \(90^\circ\).