The diagram shows four angles at a point. Work out... | Mathematics 0580 | Paper 3 Mock 01 | Calculator (Core)

Question 1 Report

The diagram shows four angles at a point.

Work out the range of the sizes of these four angles.

Answer

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.

Read lesson note on Averages And Range (CIE)

Answer Details

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].

Read lesson note on Averages And Range (CIE)

Averages And Range

View Answer

The diagram shows four angles at a point. Work out the range of the sizes of these four angles.

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