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Angles on a Straight Line and at a Point

Maths · Stage 3
Year 5
Lesson Guide
Explanation
Angles are named by size: acute under ninety degrees, right exactly ninety, obtuse between ninety and one hundred and eighty, straight one hundred and eighty, and reflex anything more than that up to a full turn of three hundred and sixty. A quarter turn is ninety, a half turn one hundred and eighty, three quarters two hundred and seventy. The name is a sanity check on your arithmetic: if you work out an angle as one hundred and forty-five and the picture shows an acute angle, something is wrong.
Your Turn
Name these: 65°, 145°, 200°. Check: acute, obtuse, reflex.
Watch Out
Obtuse stops at 180°. An angle of 200° is reflex, not obtuse.
Explanation
Angles that sit side by side on a straight line fill a half turn, so they add to one hundred and eighty degrees. If one is a hundred and twenty-five, the other is fifty-five. With three angles on the line, subtract them all: a hundred and eighty take forty take ninety leaves fifty. Then check the picture — fifty-five should look acute, and it does.
Your Turn
Three angles on a straight line: 40°, 90° and x. Find x. Check: 180 − 130 = 50°.
Watch Out
The angles must be on the SAME side of the line and meet at the same point to add to 180°.
Explanation
Angles that meet at a point and go all the way round add to three hundred and sixty degrees, a full turn. With a hundred and a hundred and ten known, the missing one is three hundred and sixty minus both, a hundred and fifty. Four angles at a point work the same way: ninety, ninety and eighty leave a hundred. Subtract everything you know from the full turn.
Your Turn
Four angles at a point: 90°, 90°, 80° and y. Find y. Check: 360 − 260 = 100°.
Watch Out
Use 360° only when the angles go all the way round. On a line it is 180°. Check the picture first.
Explanation
When two of the angles are marked equal, subtract the known ones first and then share what is left. On a line with a forty-degree angle and two equal angles: a hundred and eighty minus forty is a hundred and forty, halved is seventy each. Three equal angles at a point are a hundred and twenty each. Always check by adding back — forty plus seventy plus seventy is a hundred and eighty.
Your Turn
Two equal angles at a point, plus an angle of 100°. Find each equal angle. Check: (360 − 100) ÷ 2 = 130°.
Watch Out
Subtract BEFORE halving. Halving 180 and then subtracting 40 gives 50, which does not add back to 180.
Explanation
Three rules cover the chapter: a line is a hundred and eighty, a point is three hundred and sixty, and equal unknowns are found by subtracting then dividing. Turns behave like the same arithmetic — a quarter turn and another thirty degrees is a hundred and twenty, and turning ninety twice then forty-five back leaves a hundred and thirty-five. Quiz and exercises now.
Your Turn
You turn 90° clockwise twice, then 45° anticlockwise. How far from where you started? Check: 180 − 45 = 135°.
Watch Out
Decide first whether the picture is a line or a point. The wrong total makes every answer wrong.
📌 Key Points — this lesson in a nutshell
  • By size: acute under 90°, right exactly 90°, obtuse between 90° and 180°, straight 180°, reflex over 180°.
  • Angles on a straight line add to 180°. The missing one is 180 minus the rest.
  • Angles at a point add to 360°. A full turn.
  • If two unknown angles are marked equal, subtract the known ones first, then halve what is left.
Step 1: Introduction
Step 1 of 5
Acute, right, obtuse, straight, reflex 50°acute (under 90°) 90°right (90°) 130°obtuse (90°–180°) A straight angle is 180° — a half turn. A reflex angle is more than 180° but less than 360°. A quarter turn is 90°, a half turn 180°, three-quarters 270°, a full turn 360°. 65° acute. 90° right. 145° obtuse. 200° reflex. The name tells you roughly how big the answer should be — a quick check that your arithmetic is sane.
Two angles on a line 125°? 180°− 125°55° The two angles fill a half turn, so they add to 180°. The missing one is 180 − 125 = 55°. Three angles on a line, 40° and 90° known: the third is 180 − 40 − 90 = 50°. Check the size names: 55° should look acute, and it does.
Angles round a point 100°110°? 360°− 100°260°− 110°150° All the way round is a full turn: 360°. The missing angle is 360 − 100 − 110 = 150°. Four angles at a point, 90°, 90° and 80° known: the fourth is 360 − 260 = 100°.
Two equal angles on a line with a 40° angle 40°xx 180°− 40°140°÷ 2x = 70° Take the known angles off first, then share what is left between the equal ones. Three equal angles at a point: 360 ÷ 3 = 120° each. Two equal angles at a point with a 100° angle: (360 − 100) ÷ 2 = 130°. Check by adding back: 40 + 70 + 70 = 180 ✓.
Reading the question On a line: 125° and x. Find x.55° At a point: 100°, 110° and y. Find y.150° A door swings a quarter turn, then another 30°. Total?120° Turn 90° clockwise twice, then 45° back. Total turn?135° Line → 180. Point → 360. Equal unknowns → subtract, then divide. Turns add and subtract: 90 + 90 − 45 = 135. Quiz and exercises now.
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