The diagram shows four angles at a point. Work out the range of the sizes of these four angles.
Question 1 Report
The diagram shows four angles at a point.
Work out the range of the sizes of these four angles.
Answer Details
This question combines an angle fact with a statistics definition. Three of the four angles at the point are given as \(85^\circ\), \(97^\circ\) and \(63^\circ\), and the fourth must be found before the range can be worked out.
Angles at a point add up to \(360^\circ\), so the fourth angle is
\[ y=360-(85+97+63)=360-245=115 \][M1], that is \(115^\circ\).
The four angles are now \(85^\circ\), \(97^\circ\), \(63^\circ\) and \(115^\circ\). The range is the largest minus the smallest:
\[ 115-63=52 \]so the range of the sizes of the four angles is \(52^\circ\) [A1].
The missing angle turns out to be the largest of the four, so it must be included when picking the extremes; taking the range of only the three given angles would give \(97-63=34^\circ\). Note also that angles on a straight line sum to \(180^\circ\) while angles at a point sum to \(360^\circ\), and using the wrong fact here would make the fourth angle negative, which is an immediate signal that something has gone wrong.
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