Stage 11 · Shape & space
Angles
Line 180°, point 360°, right angle 90°.
How to do it
Method
Line 180°, point 360°, right angle 90°
130 + 150 = 280, 360 − 280 = 80
Another way
Take each away
360 − 130 − 150 = 80
In full
Use what the angles make together: angles on a straight line (a straight angle) make 180°, angles round a point (a round angle) make 360°, and a right angle is 90°. So x is the total less the angles you know: 50° on a straight line, 180 − 50 = 130, x = 130°. Quicker: add the known angles first, then take away once: 130° and 150° round a point, 130 + 150 = 280, 360 − 280 = 80, x = 80°. Another way: take the known angles away one by one: 360° − 130° − 150° = 80° — the same answer.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
∠x = ?°
Show the answer and working
Answer: ∠x = 15°
A right angle is 90°: 90 − 75 = 15, so x = 15°
Example 2
∠x = ?°
Show the answer and working
Answer: ∠x = 150°
Angles on a straight line make 180°: 180 − 30 = 150, so x = 150°
Example 3
∠x = ?°
Show the answer and working
Answer: ∠x = 235°
Angles round a point make 360°: add the angles you know first, 75 + 50 = 125, 360 − 125 = 235, so x = 235°
Example 4
∠x = ?°
Show the answer and working
Answer: ∠x = 202°
Angles round a point make 360°: add the angles you know first, 105 + 53 = 158, 360 − 158 = 202, so x = 202°
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