Adjacent, complementary, supplementary and vertically opposite angles; angles round a point
Mathematics Prep 1 Term 1, Unit 4, Lessons 1–2
GoalUse the relations between angles to find unknown angles, with equations in x.
New words
adjacent angles · two angles with a common vertex and a common side, on different sides of itcomplementary · two angles whose sum is 90°supplementary · two angles whose sum is 180°vertically opposite · the equal angles opposite each other where two lines cross
Explanation
Adjacent angles share a vertex and a side but do not overlap. Two angles are complementary if they add up to 90°, so the complement of 35° is 55°. They are supplementary if they add up to 180°, so the supplement of 35° is 145°. Two supplementary angles need not be adjacent. When two straight lines cross, the angles opposite each other are vertically opposite and equal; the angles next to each other add up to 180°. The angles around a point add up to 360°. To find unknown angles, write an equation with x and solve it, then check that the angles make sense.
★Remember
Complementary: 90°. Supplementary: 180°. Vertically opposite: equal. Around a point: 360°.
Worked examples
Complement and supplement. The complement of 35° is 90° − 35° = 55°. The supplement of 35° is 180° − 35° = 145°. Check: 35 + 55 = 90 and 35 + 145 = 180.
Two lines cross and one angle is 70°. The angle opposite it is also 70° (vertically opposite). The angles next to it are 180° − 70° = 110°. Check: 70 + 110 + 70 + 110 = 360°.
Round a point. The angles are 2x, 3x, 90° and 70°. Their sum is 360°, so 2x + 3x + 90 + 70 = 360. Then 5x + 160 = 360, 5x = 200 and x = 40. The angles are 80°, 120°, 90° and 70°. Check: 80 + 120 + 90 + 70 = 360.
Class activity
Paper angles. With a grown-up, fold a sheet to make a right angle, then fold the corner in half to make 45°. Show a pair of complementary angles and a pair of supplementary angles on the paper.
Practice
1
Find the complement of 62° and the supplement of 105°.
90° − 62° = 28° and 180° − 105° = 75°.
2
Two lines cross and one angle is 48°. Find the other three angles.
The opposite angle is 48°. The two others are 180° − 48° = 132° each.
3
Two adjacent angles on a straight line are x and 2x. Find them.
x + 2x = 180, so 3x = 180 and x = 60. The angles are 60° and 120°.
4
Angles round a point are 3x, 5x and 120°. Find x and the angles.
8x + 120 = 360, 8x = 240, x = 30. The angles are 90°, 150° and 120°.
5
Seif solves 2x − 12 = 90 and writes 2x = 78. What is wrong? Find x.
