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Polygons and Geometrical Constructions

Secondary 1 practice

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Polygons and Geometrical Constructions practice questions

Secondary 1 topics, the foundation the O-Level Mathematics 4052 syllabus builds on. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

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What this topic covers

Worked examples

Example 1

An isosceles triangle has base angles of 55°55° each. Find the angle between the two equal sides.
x55°Not drawn to scale
Show the worked solution
  • Base angles of isosceles triangle are equal(base ∠s, isos. △)\text{Base angles of isosceles triangle are equal} \quad (\text{base } \angle\text{s, isos. } \triangle)
  • Angle between the equal sides=180°−2×55°(∠ sum of △)\text{Angle between the equal sides} = 180° - 2 \times 55° \quad (\angle\text{ sum of } \triangle)
  • =180°−110°= 180° - 110°
  • =70°= 70°

Answer: 7070

Example 2

In rhombus ABCDABCD, diagonal BDBD is drawn. Given that ∠ABD=70°\angle ABD = 70°, find ∠ABC\angle ABC.
70°xABCDNot drawn to scale
Show the worked solution
  • Diagonal bisects ∠ABC(property of rhombus)\text{Diagonal bisects } \angle ABC \quad (\text{property of rhombus})
  • ∠ABC=2×∠ABD\angle ABC = 2 \times \angle ABD
  • =2×70°= 2 \times 70°
  • =140°= 140°

Answer: 140140

Example 3

All interior angles of a polygon are 115°115° except one angle which is 80°80°. Find the number of sides.
Show the worked solution
  • (n−1)×115+80=(n−2)×180(∠ sum of polygon)(n - 1) \times 115 + 80 = (n - 2) \times 180 \quad (\angle\text{ sum of polygon})
  • 115n−35=180n−360115n - 35 = 180n - 360
  • 325=65n325 = 65n
  • n=32565n = \frac{325}{65}
  • =5= 5

Answer: 55

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Which syllabus does this follow?

O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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