Angle relationships
You rarely measure an angle with a protractor in algebra — you reason it out. A handful of rules let you find a missing angle from the ones around it, turning a diagram into a quick subtraction.
Lines and points
Angles that sit together on a straight line add up to 180° (they are called supplementary), so if one is 120° the other is 180 − 120 = 60°. Angles that meet all the way around a point add up to 360°. Two angles that make a right angle are complementary and add up to 90°.
Crossing lines
When two straight lines cross, the angles directly across from each other — the vertically opposite angles — are equal. So if one angle at the crossing is 70°, the one opposite it is also 70°.
Inside a triangle
The three angles of any triangle add up to 180°, so a triangle with angles of 50° and 60° has a third angle of 180 − 50 − 60 = 70°. In an isosceles triangle the two base angles are equal, so they share whatever is left after the apex: an apex of 40° leaves 140°, giving base angles of 70° each.
Parallel lines
When a line crosses a pair of parallel lines, matching positions give equal angles: corresponding angles are equal, and alternate angles (the “Z” pair) are equal. Co-interior angles (the “C” pair, on the same side) are supplementary and add up to 180°.
How to type your answer
Enter the size of the angle as a number of degrees, like 70. You can add a degree symbol (70°) if you like — it's read the same way.
Practice
Warming up your practice…