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Lines Angles and Polygons — Free MYP5 Mathematics (Standard) Practice Questions
1QuestionInterior and Exterior Angles of PolygonsConcept Practice
2 marks~3 minCriterion A
A landscape architect is designing a public courtyard floor using a single type of regular polygon as the tile shape.
a
Explain why a regular hexagon can tile a floor without gaps or overlaps, referring to its interior angle. [1]
b
Discuss one limitation of restricting the tile design to a single type of regular polygon. [1]
Solutions
2QuestionParallel Lines and TransversalsAssessment Practice
4 marks~6 minCriterion D
A road engineer is designing two parallel lanes of a highway intersected by a slip road acting as a transversal. The angle formed between the slip road and the near lane is . The corresponding angle at the far lane is .
a
Deduce an equation relating the two angles and solve for . [2]
b
Justify whether the slip road crosses both lanes at an acute or obtuse angle, using the calculated angle measure. [1]
c
The highway design requires that no approach angle exceeds for driver safety. Advise the engineer whether this design should be approved. [1]
Solutions
3QuestionProperties of Regular and Irregular PolygonsConcept Practice
2 marks~3 minCriterion C
A landscape architect is designing a pavilion with a regular hexagonal floor plan. Each interior angle of the floor must be equal for the tiling to fit correctly.
a
Calculate the sum of the interior angles of a hexagon. [1]
b
The architect claims each interior angle measures 130°. Justify whether this claim is correct. [1]
Solutions
4QuestionProperties of Regular and Irregular PolygonsAssessment Practice
2 marks~3 minCriterion B
A landscape architect is designing decorative paving tiles, each shaped as a regular polygon. The table below shows the sum of interior angles for polygons with 3 to 8 sides.
The architect needs a tile shaped as a regular decagon (10 sides).
| Number of sides | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|
| Sum of interior angles (°) | 180 | 360 | 540 | 720 | 900 | 1080 |
The architect needs a tile shaped as a regular decagon (10 sides).
a
Deduce the general rule for the sum of interior angles of a polygon with sides. [1]
b
The architect states: "A regular decagon tile will have interior angles greater than 135°, making it unsuitable for corner paving." Justify whether this statement is correct. [1]
Solutions
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