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Two angles of a convex polygon measure 100$ °$ and 140$ °$ respectively. All the other angles are equal and measure 120$ °$ . The number of sides in this particular polygon is .

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Important Questions on Understanding Quadrilaterals

MEDIUM

The number of sides of two regular polygons is in the ratio 5 : 4. The difference between their interior angles is 9°. Consider the following statements:

1) One of them is a pentagon and the other is a rectangle.

2) One of them is a decagon and the other is an octagon.

3) The sum of their exterior angles is 720°.

Which of the above statements is/are correct?

EASY

Perimeter of the rectangle in the figure is 36 centimetresAC=164 centimetres. Find length of AB.

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EASY

In triangle ABC, A=B=30°, AC=4 centimetres. What is the length of BC?

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EASY

Given that the angles of a polygon are all equal and each angle is a right angle.

Statement-1: The polygon has exactly four sides.

Statement-2: The sum of the angles of a polygon having n sides is (3n-8) right angles.

Which one of the following is correct in respect of the above statements?

MEDIUM
The sum of interior angles of a regular polygon is 1260°. What is the difference between an exterior angle and an interior angle of the polygon:
MEDIUM
A closed polygon has six sides and one of its angles is 30° greater than each of the other five equal angles. What is the value of one of the equal angles?
EASY

Perimeter of the rectangle in the figure is 36 centimetresAC=164 centimetres. What is AB+BC

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HARD
A point P in the interior of a regular hexagon is at distance 8,8,16 units from three consecutive vertices of the hexagon, respectively. If r is radius of the circumscribed circle of the hexagon, what is the integer closest to r?
EASY
If each interior angle of a regular polygon is 12847°, then what is the sum of the number of its diagonals and number of its sides?
EASY
Two sides of a regular polygon with n sides, when extended, meet at an angle of 28°. What is the smallest possible value of n?
HARD
What is the diameter of a circle inscribed in regular polygon of 15 sides with side length unity?
MEDIUM
 The exterior angle of a regular polygon is 72°. What would be the sum of all its interior angles?
EASY

In the figure, B=90°, C=44°

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What is the measure of A?

EASY
What is the magnitude (in radian) of the interior angle of a regular pentagon?
EASY
If the area of a regular hexagon is 1083 cm2 , its perimeter is_____.
HARD
Let t be the area of a regular pentagon with each side equal to 1. Let P(x)=0 be the polynomial equation with least degree, having integer coefficients, satisfied by x=t and the gcd of all the coefficients equal to 1 . If M is the sum of the absolute values of the coefficients of P(x). What is the integer closest to M? sin18°=5-14
MEDIUM

If the measure of each exterior angle of a regular polygon is 5137, then the ratio of the number of its diagonal to the number of its side is:

EASY

If the interior angle of a regularpolygon is 108°, then it is a-

1. Octagon

2. Hexagon

3. Pentagon

4. Tetragon 

MEDIUM

In the figure below, the measure of ∠$ \text{a}$=_____$ \text{°}$.

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