1 Marks Question

Question 11 Mark

Fill in the blanks.
For a convex polygon of $n$ sides, we have:
Sum of all exterior angles = ______.

Answer

Sum of all exterior angles $= 360^\circ .$

Question 21 Mark

Write $'T'$ for true and $'F'$ for false for the following: The diagonals of a rectangle are perpendicular to each other.

Answer

False. Solution: The diagonals of a rectangle are not perpendicular to each other.

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Question 31 Mark

Fill in the blanks. For a convex polygon of $n$ sides, we have: Sum of all interior angles $=$ ______.

Answer

Sum of all interior angles $= (n - 2) \times 180^\circ .$

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Question 41 Mark

Fill in the blanks. For a regular polygon of $n$ sides, we have: Sum of all interior angles $=$ ______.

Answer

Sum of all interior angles $= (n - 2) \times 180^\circ .$
Solution: Sum of all exterior angles of a regular polygon is $360^\circ .$

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Question 51 Mark

Fill in the blanks. For a regular polygon of n sides, we have: Sum of all exterior angles $=$ ______.

Answer

Sum of all exterior angles $= 360^\circ .$
Solution: Sum of all exterior angles of a regular polygon is $360^\circ .$

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Question 61 Mark

Fill in the blanks. Each exterior angle of a regular polygon is $60^\circ .$ This polygon is a ______.

Answer

Each exterior angle of a regular polygon is $60^\circ .$ This polygon is a $6.$
Solution: Each exterior angle of a regular polygon is $60^\circ .$
$\therefore\frac{360}{60}=6$
Therefore, the given polygon is a hexagon.

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Question 71 Mark

Fill in the blanks. A pentagon has ______ diagonals.

Answer

A pentagon has $5$ diagonals.
Solution: If n is the number of sides,
the number of diagonals $=\frac{\text{n}(\text{n}-3)}{2}$
$=\frac{5(5-3)}{2}$
$=5$

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Question 81 Mark

Define the terms: Open curve.

Answer

Open curve: An open curve is a curve where the beginning and end points are different. Example: Parabola.

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Question 91 Mark

Define the terms: Simple closed curve.

Answer

Simple closed curve: A closed curve that does not intersect itself.

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Question 101 Mark

Write $'T'$ for true and $'F'$ for false for the following:
Every rhombus is a kite.

Answer

Adjacent sides of a kite are equal and this is also true for a rhombus. Additionally, all the sides of a rhombus are equal to each other.

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Question 111 Mark

Fill in the blanks. For a convex polygon of $n$ sides, we have: Number of diagonals $=$ ______.

Answer

Number of diagonals $=\frac{\text{n}(\text{n}-3)}{2}.$

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Question 121 Mark

Define the terms: Closed curve.

Answer

Closed Curve: A curve that joins up so there are no end points. Example: Ellipse.

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Question 131 Mark

Fill in the blanks. The sum of all interior angles of a regular hexagon is $($_____$)^\circ .$

Answer

The sum of all interior angles of a regular hexagon is $(720)^\circ .$
Solution:
Sum of the interior angles of a regular hexagon $= (6 - 2) \times 180^\circ = 720^\circ .$

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Question 141 Mark

Fill in the blanks. Each interior angle of a regular polygon is $108^\circ .$ This polygon is a ______.

Answer

Each interior angle of a regular polygon is $108^\circ .$ This polygon is a $360^\circ .$
Solution:
If the interior angle is $108^\circ ,$
then the exterior angle will be $72^\circ .$ (interior and exterior angles are supplementary) Sum of the exterior angles of a polygon is $360^\circ .$
$72\text{n}=360$
$\text{n}=\frac{360}{72}$
$\text{n}=5$
Since it has $5$ sides, the polygon is a pentagon.

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Question 151 Mark

Write $'T'$ for true and $'F'$ for false for the following: The diagonals of a parallelogram are equal.

Answer

The diagonals of a parallelogram need not be equal in length.

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Question 161 Mark

Fill in the blanks. Each interior angle of a regular octagon is $($_____$)^\circ .$

Answer

Each interior angle of a regular octagon is $(135)^\circ .$
Solution: Octgon has $8$ sides.
$\therefore$ Interior angle $=\frac{180^\circ\text{n}-360^\circ}{\text{n}}$
Interior angle $=\frac{(180^\circ\times8)-360^\circ}{{8}}=135^\circ$

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Question 171 Mark

Write $'T'$ for true and $'F'$ for false for the following: The diagonals of a rhombus bisect each other at right angles.

Answer

True.

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