Understanding Quadrilaterals Test

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Understanding Quadrilaterals Test - 2

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Question 1
1 / -0

What will be the sum of the smallest and greatest angles of the quadrilateral, if it's angles are in the ratio of 2 : 3 : 3 : 4?

A
150°

B
160°

C
170°

D
180°

Solution

Let the angles be 2x, 3x, 3x, 4x.
Sum of the angles of a quadrilateral = 360°

2x + 3x + 3x + 4x = 360°
12x = 360°
x = 30°

Required sum of angles = 2x + 4x = 6x = 6(30°) = 180°
Question 2
1 / -0

A rhombus which only has right angles is said to be a

A
square

B
rectangle

C
parallelogram

D
kite

Solution

A rhombus which only has right angles is said to be a square as it will have all the properties of a square.
Question 3
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Which of the following can be the measure of exterior angle of a regular polygon?

A
27°

B
60°

C
37°

D
16°

Solution

60° can be the measure of exterior angle of a regular polygon as it is a factor of 360°, however other given angles cannot be for the same reason.
Question 4
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A park is in the shape of a triangle of perimeter 120 m. What could be the possible lengths of all the three sides?

A
30 m, 50 m, 40 m

B
80 m, 20 m, 20 m

C
20 m, 30 m, 70 m

D
25 m, 65 m, 30 m

Solution

The park is in the shape of a triangle; and in a triangle, the sum of any two sides is more than the third side.
Since perimeter is the sum of all the sides;

Possible sum = 30 + 50 + 40 = 120 m
Hence, the only possible sides are 30 m, 50 m and 40 m.
Question 5
1 / -0

Rohan is playing in a garden which is in the shape of a quadrilateral. He observes that only one pair of opposite sides is parallel. So, what is the shape of the garden?

A
Square

B
Rectangle

C
Trapezium

D
Parallelogram

Solution

A square is a flat shape with 4 equal sides and every angle is a right angle. Also both pair of opposite sides are parallel.
A rectangle is a four-sided flat shape where every angle is a right angle. Also both pair of opposite sides are parallel and of equal length.

A parallelogram has both pair of opposite sides parallel and equal in length. Also opposite angles are equal.
Only trapezium has only 1 pair of opposite sides parallel. Hence, it is a trapezium.