Angle Properties of Polygons
You're viewing free preview questions — 4 questions previewing here — subscribe to unlock 35 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

Angle Properties of Polygons — Free MYP4 Mathematics (Extended) 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 360°360°.

Using the formula S=(n−2)×180°S = (n-2) \times 180°, where nn 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]
Question diagram

Solutions

2QuestionParallel Lines and TransversalsAssessment Practice
2 marks~3 minCriterion C
Elm Street and Oak Street are parallel. Maple Avenue crosses both streets as a transversal, forming eight angles at the two intersections. At the intersection with Elm Street, the angle on the upper-right measures 65°65°.
a
State the measure of the corresponding angle at the intersection with Oak Street. [1]
b
A city planner claims that Maple Avenue crosses both streets "at the same angle," using this as evidence that the streets are parallel. Justify whether this claim constitutes valid geometric evidence of parallelism. [1]
Question diagram

Solutions

3QuestionInterior and Exterior Angles of PolygonsAssessment Practice
4 marks~6 minCriterion D
A construction company is designing a floor using a tessellating pattern of regular hexagons and equilateral triangles, where exactly two hexagons and two triangles meet at every vertex.
a
Calculate the interior angle of a regular hexagon and the interior angle of an equilateral triangle. [2]
b
Show that two regular hexagons and two equilateral triangles can meet at a vertex without gaps or overlaps. [1]
c
The site engineer claims this mathematical model "guarantees a perfect fit on any real floor." Advise the engineer whether this claim should be used to guide the physical installation, referring to at least two practical factors. [1]
Question diagram

Solutions

4QuestionInterior and Exterior Angles of PolygonsAssessment Practice
12 marks~18 minCriterion B
A designer is tiling a floor using identical regular polygon tiles that fit together edge-to-edge with no gaps. For tiles to tessellate, the interior angle must divide exactly into 360°.

The interior angle of a regular nn-sided polygon is given by

A=180(n−2)n degreesA = \frac{180(n-2)}{n} \text{ degrees}

and the sum of interior angles by S=180(n−2)S = 180(n-2) degrees.
a
Calculate the sum of interior angles of a regular 20-sided polygon. [2]
b
Deduce a formula for the exterior angle EE of a regular nn-sided polygon in terms of nn, showing your reasoning clearly. [3]
c
A tile has an interior angle of 150°. Calculate the number of sides of this tile. [3]
d
Justify whether the 150° tile can tessellate a floor on its own, using your results from parts (b) and (c). [4]

Solutions

Questions 5-39

Unlock these questions with Premium

Sign Up →

That's every free question here — 4 of 39.

+35 more questions, plus Mock Papers & Worksheets, are waiting in Premium.

Upgrade