Angles at a point and on a line
Objective. Use 360° at a point and 180° on a straight line.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Angles at a point around a single vertex always add up to 360°, while angles that lie along a single straight line always add up to 180°. These two facts allow missing angles to be calculated when some angles are already known. For example, if three angles meeting at a point are 110°, 95° and an unknown angle, the unknown equals 360−110−95=155°. Similarly, if two angles lie on a straight line and one is 65°, the other must be 180−65=115°, since together they form a straight line.
Worked example
Three angles meet at a point: 95°, 140° and an unknown angle x. Find the value of x.
- 1Recall angles at a point sum to 360°.
- 2Add the known angles: 95+140=235.
- 3Subtract from 360: 360−235=125.
- 4State the value of x.
Answer: x = 125°
Concept mastery
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Practice
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Start practisingCommon mistake. Pupils sometimes use 180° for angles meeting at a point instead of 360°, giving an answer that is too small. Always check whether the angles form a full point or just a straight line before subtracting.
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