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Lines Angles and Polygons — Free MYP4 Mathematics (Standard) Practice Questions
1QuestionInterior and Exterior Angles of PolygonsConcept Practice
2 marks~3 minCriterion A
Architects designing a tiled floor use regular hexagonal tiles. For tiles to fit together without gaps, the interior angles at each vertex must sum to exactly .
Using the formula , where is the number of sides, calculate the sum of the interior angles of a regular hexagon and hence find one interior angle. [1]
Justify whether a regular hexagon can tile a flat floor without gaps, using your calculated interior angle. [1]
Using the formula , where is the number of sides, calculate the sum of the interior angles of a regular hexagon and hence find one interior angle. [1]
Justify whether a regular hexagon can tile a flat floor without gaps, using your calculated interior angle. [1]
Solutions
2QuestionTypes of Angles and Angle RelationshipsAssessment Practice
6 marks~9 minCriterion D
A ship navigates a narrow channel using triangulation. The captain measures the angle to landmark A as and the angle to landmark B as . The straight-line distance between A and B along the shore is .
a
Identify two sources of error in this triangulation method — one instrumental and one environmental — and explain how each may affect the accuracy of the ship's estimated position. [2]
b
Analyse how the geometric configuration of the triangle formed by the ship and the two landmarks affects the precision of the position fix, referring to the angles given. [2]
c
The captain considers switching to GPS, which has a typical positional accuracy of . Advise the captain on whether GPS should replace triangulation entirely for this channel crossing, justifying your recommendation with reference to both methods' limitations. [2]
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
4QuestionTypes of Angles and Angle RelationshipsConcept 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 relationship between the number of sides and the sum of interior angles.
The architect needs a tile with a sum of interior angles of exactly and is considering an octagonal tile.
| Number of sides | 3 | 4 | 5 | 6 |
|---|---|---|---|---|
| Sum of interior angles (°) | 180 | 360 | 540 | 720 |
The architect needs a tile with a sum of interior angles of exactly and is considering an octagonal tile.
a
Deduce the relationship between the number of sides and the sum of interior angles. [1]
b
Justify whether an octagonal tile satisfies the architect's requirement. [1]
Solutions
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