Compare — 3 marks
An architect is designing two separate roof structures for a building. The first roof is formed by two straight beams meeting at a point, creating angles on a straight line. The second roof uses three beams meeting at a single point on the ground. The architect needs to compare angle properties in these two configurations to ensure structural stability.
-
(a) In the first roof design, two beams meet at a point on a straight wall. One beam makes an angle of \(58°\) with the wall. Calculate the angle that the other beam makes with the wall on the same side of the line.
[1 mark]
-
(b) In the second roof design, three beams meet at a point on the ground. The angles between consecutive beams are \(115°\), \(128°\), and a third angle. Compare the angle properties used in the first design (angles on a straight line) with those needed in the second design (angles around a point). Calculate the third angle and explain which angle rule applies to each design.
[2 marks]
Show mark scheme
- (a) Correctly applies angles on a straight line sum to \(180°\) to find the answer as \(122°\)
- (b) Correctly calculates the third angle as \(117°\) using angles around a point sum to \(360°\)
- (b) Clearly compares both angle rules: identifies that the first design uses 'angles on a straight line = \(180°\)' while the second design uses 'angles around a point = \(360°\)', recognising these are different geometric properties
Suggest — 4 marks
An architect is designing a roof truss system for a building. The design involves several straight beams that intersect at various points. One critical joint in the truss has three beams meeting at a single point. Two of the beams form angles with a horizontal reference line, and the architect needs to verify that the angles satisfy geometric constraints before construction begins.
-
(a) At a joint in the truss, two straight beams meet and form an angle of \(47°\) between them. A third beam is positioned so that it lies on the opposite side of one of the original beams, forming a straight line. Calculate the angle between the third beam and the second original beam. Suggest what angle property you have used to find your answer.
[2 marks]
-
(b) At another joint, four beams meet at a point. Three of the angles formed around this point are \(85°\), \(92°\), and \(78°\). Suggest what the fourth angle must be, and explain which angle property justifies your answer. You must show your working.
[2 marks]
Show mark scheme
- (a) Calculates the angle as \(180° - 47° = 133°\)
- (a) Identifies and states the angle property: angles on a straight line sum to \(180°\) (or equivalent wording such as 'angles on a line' or 'supplementary angles')
- (b) Calculates: \(360° - (85° + 92° + 78°) = 360° - 255° = 105°\)
- (b) Suggests the fourth angle is \(105°\) and identifies the property: angles around a point sum to \(360°\) (or equivalent wording such as 'angles around a point' or 'angles at a point')
GCSE Perfect