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Mathematics · Angles and geometry

Adjacent, complementary and supplementary angles

When a road splits in two, how are the angles it makes related? Explore adjacent angles, complementary angles that add up to 90° and supplementary angles that add up to 180°, using cycle lanes and ramps.

  • 20 min
  • 1 simulation
  • Mini quiz

Updated:

Preview

The question

The town's main street runs perfectly straight. At one point a new cycle lane branches off it, making an angle of 55∘55^\circ with the street. On the other side of the cycle lane there is another angle between it and the street. Can you find this second angle without measuring? Hint: the street itself is a straight line.

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Protractor

The supplement of 55°

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Prediction

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What type of angle do you think the adjacent supplementary angle next to a 55° angle is?

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Frequently asked

5 questions

How do I stop mixing up complementary and supplementary?

Complementary angles add up to 90°, supplementary angles add up to 180°. Memory tip: C comes before S in the alphabet, just as 90 comes before 180; complementary makes a corner (90°), supplementary makes a straight line (180°). After solving, add the two angles and check whether you get 90 or 180.

Do complementary or supplementary angles have to be next to each other?

No. Two angles that add up to 90° are complementary even if they are far apart, such as 30° and 60°. Two angles that sit side by side on a straight line have a special name: adjacent supplementary angles.

Do adjacent angles always add up to 180°?

No. Adjacent angles are simply angles that share a vertex and one arm and do not overlap; their measures can be anything. They add up to 180° only when their outer arms form a straight line.

Why is the supplement of an angle found with 180° − x?

A straight line is half a turn, or 180°. A ray drawn from a point on the line splits it into two angles; as one grows the other shrinks, but together they always make 180°. That is why the angle next to a 55° angle is 180° − 55° = 125°.

Does every angle have a complement?

No. Complementary angles add up to 90°, so an angle with a complement must be less than 90°; a 120° angle has no complement. For the same reason an angle with a supplement must be less than 180°: the supplement of 120° is 60°.