Class 9 Rectilinear Figures (Quadrilaterals and Polygons) Mock Test (ICSE)

Topics in Rectilinear Figures (Quadrilaterals and Polygons)

• Sum of interior and exterior angles of a polygon
• Regular polygons
• Properties of parallelogram, rectangle, rhombus and square
• Proofs on quadrilaterals

Rectilinear Figures (Quadrilaterals and Polygons) practice questions with answers

1. Q1Multiple choice·1 mark
   If the diagonals of a rhombus are $12\text{ cm}$ and $16\text{ cm}$, then the length of its side is:

   1. (a)14 cm
   2. (b)8 cm
   3. (c)10 cm
   4. (d)20 cm
   Show answer and step marks

   1. Correct option: (c) Side of rhombus $s = \sqrt{\left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2} = \sqrt{6^2 + 8^2} = \sqrt{100} = 10\text{ cm}$.+1

   Answer: (c)
2. Q2Multiple choice·1 mark
   The sum of the interior angles of a regular polygon is $1080^\circ$. The number of sides of the polygon is:

   1. (a)$6$
   2. (b)$10$
   3. (c)$7$
   4. (d)$8$
   Show answer and step marks

   1. Correct option: (d) $8$+1

   Answer: (d)
3. Q3Multiple choice·1 mark
   If the diagonals of a parallelogram are equal and bisect each other at right angles, then the most specific name for the quadrilateral is:

   1. (a)Rectangle
   2. (b)Rhombus
   3. (c)Square
   4. (d)Kite
   Show answer and step marks

   1. Correct option: (c) Square. Equal diagonals make it a rectangle and perpendicular diagonals make it a rhombus, so it is a square.+1

   Answer: (c)
4. Q4Long answer·4 marks
   The measure of each interior angle of a regular polygon is $5$ times the measure of its exterior angle. (a) Find the measure of each exterior angle and each interior angle. (b) Find the number of sides of the polygon. (c) Find the sum of all the interior angles of this polygon.
   Show answer and step marks

   1. Let the exterior angle of the regular polygon be $x$. Then the interior angle is $5x$. Since the interior and exterior angles are supplementary, $x + 5x = 180^\circ$.+1
   2. Solving for $x$, $6x = 180^\circ \implies x = 30^\circ$, so the exterior angle is $30^\circ$.+0.5
   3. The interior angle is $5 \times 30^\circ = 150^\circ$.+0.5
   4. The number of sides $n$ is given by $n = \frac{360^\circ}{\text{Exterior angle}} = \frac{360^\circ}{30^\circ} = 12$.+1
   5. The sum of all interior angles $= (n - 2) \times 180^\circ = (12 - 2) \times 180^\circ = 10 \times 180^\circ = 1800^\circ$.+1

   Answer: Exterior angle: $30^\circ$, Interior angle: $150^\circ$, Number of sides: $12$, Sum of interior angles: $1800^\circ$

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