The exterior angle of a triangle, the angle sum of a quadrilateral, and the properties of the special quadrilaterals.
What you will learn
- Use the exterior angle of a triangle
- Use the angle sum of a quadrilateral (360°)
- Use the properties of parallelograms, kites, rhombuses and trapeziums
Exterior angles and quadrilaterals
The interior angles are the angles inside a shape.
Extend one side of a triangle past a corner and the angle between the extension and the next side is an exterior angle. The exterior and interior angles at that corner are on a straight line, so they add to 180°.
- The exterior angle of a triangle equals the sum of the two interior angles opposite it. With interior angles 50° and 70° opposite it, the exterior angle is 50 + 70 = 120°.
- Angles in a quadrilateral add up to 360° (two triangles). With angles 90°, 80° and 110°, the fourth is 360 − 90 − 80 − 110 = 80°.
With algebra, add all the angles and set the total equal to 180° (triangle) or 360° (quadrilateral). An isosceles triangle with base angles x° each and top angle (2x + 20)° gives x + x + 2x + 20 = 180, so 4x = 160 and x = 40. Remember there are two base angles. A quadrilateral with angles x, 2x, 3x and (x + 10)° gives 7x + 10 = 360, so x = 50.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Exterior angles and quadrilaterals
- Special quadrilaterals
7 practice questions, marked as you go; about 25 minutes in all.
Key terms
Interior, Exterior, Most specific name
In this unit: Angles, polygons and parallel lines
Angle facts on lines, at points and in triangles, angles with parallel lines, quadrilaterals, interior and exterior angles of polygons, and chains of reasoning.
- Angle facts
- Angles and parallel lines
- Triangles and quadrilaterals
- Angles in polygons
- Angle reasoning