Quadrilaterals Test

Result

Quadrilaterals Test - 11

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Weekly Quiz Competition

Question 1
1 / -0

In a quadrilateral ABCD, ∠A = 82°, ∠C = 120° and ∠D = 74°. What is the measure of ∠B?

A
80°

B
82°

C
84°

D
87°

Solution

∠A + ∠B + ∠C + ∠D = 360° (Angle sum property of a quadrilateral)
So, ∠B = 360° - 82° - 120° - 74° = 84°
Question 2
1 / -0

What is the maximum exterior angle possible for a regular polygon?

A
60^o

B
90^o

C
120^o

D
180^o

Solution

Maximum exterior angle possible = 120^o

Equilateral triangle is the regular polygon having the maximum possible exterior angle because measurement of exterior angle is inversely proportional to the number of sides of the regular polygon, and equilateral triangle is the regular polygon that has the least number of sides.

Measure of each exterior angle of a regular polygon = 360°/n
Where n is the number of sides of the polygon.

The sum of all exterior angles of a regular polygon is 360⁰.

Since 360⁰ is a constant, so the measure of each exterior angle depends on the number of sides of polygon. Lesser number of sides of polygon means higher measure of exterior angle. The regular polygon with the least number of sides is equilateral triangle.

So, the measure of each exterior angle of an equilateral triangle is the maximum =360°/3 = 120⁰
Question 3
1 / -0

Which of the following statements is/are true?

(i) The minimum exterior angle possible for a regular polygon is 60°.
(ii) The maximum exterior angle possible for a regular polygon is 120°.

A
Both (i) and (ii)

B
Only (i)

C
Only (ii)

D
Neither (i) nor (ii)

Solution

A regular polygon having 6 sides will have an exterior angle of 60^o.
Any regular polygon having sides greater than this will have an exterior angle less than 60^o.
∴ (i) is false.

Also, the minimum interior angle of a regular polygon is 60° because the minimum interior angle will be that of an equilateral triangle.

So, the maximum exterior angle = 180° - 60° = 120°
∴ (ii) is true.

Hence, (3) is the correct option.