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Geometry - Quadrilaterals and Polygons

Multiple Choice Questions

11.

If ABCD be a cyclic quadrilateral in which ∠A = 4x°, ∠B = 7x°, ∠C = 5y°, ∠D = y°, then x : y is

3 : 4
4 : 3
5 : 4
4 : 5

380 Views

12.

ABCD is a cyclic quadrilateral and AD is a diameter. If ∠DAC = 55° then value of ∠ABC is

55°
35°
145°
145°

481 Views

13.

All sides of a quadrilateral ABCD touch a circle. If AB = 6 cm, BC = 7.5 cm, CD = 3 cm, then DA is

3.5 cm
4.5 cm
2.5 cm
2.5 cm

571 Views

14.

Inside a square ABCD, ΔBEC is an equilateral triangle. If CE and BD intersect at O. then ∠BOC is equal to

60°
75°
90°
90°

302 Views

15.

Each interior angle of a regular octagon in radians is

$straight pi over 4$
$fraction numerator 3 straight pi over denominator 4 end fraction$
$fraction numerator 2 straight pi over denominator 3 end fraction$
$fraction numerator 2 straight pi over denominator 3 end fraction$

177 Views

16.

ABCD is a rectangle where the ratio of the lengths of AB and BC is 3 : 2. If P is the mid point of AB, then the value of is

$3 over 5$
$2 over 5$
$3 over 4$
$3 over 4$

266 Views

17.
If a regular polygon has each of its angles equal to $3 over 5$ times of two right angles, then the number of sides is

3

5

6

6

Each interior angle of a regular polygon
$equals space open parentheses 180 space cross times space 3 over 5 close parentheses space equals space 108 degree$
Sum of interior and exterior equals 180 degree
I + E = 180°
E = 180° - 108° = 72°
$No space of space sides space equals space open parentheses fraction numerator 360 degree over denominator Each space exterior space angle end fraction close parentheses space equals space open parentheses fraction numerator 360 degree over denominator 72 degree end fraction close parentheses space equals space 5$

177 Views

18.

The sum of all interior angles of a regular polygon is twice the sum of all its exterior angles. The number of sides of the polygon is

217 Views

19.

The ratio between the number of sides of two regular polygons is 1 : 2 and the ratio between their interior angles is 2 : 3. The number of sides of these polygons is respectively.