Directions: Study the following questions and choose the right answer:
1
ABCD is a cyclic trapezium such that AD || BC, if ∠ABC = 70°, then the value of ∠BCD is :
» Explain it
B

∠ABC + ∠CDA = 180°

∠CDA = 180° – ∠ABC = 180° – 70° = 110°

We know that,

∠BCD + ∠CDA = 180°

∴ ∠BCD = 180° – ∠CDA = 180° – 110° = 70°

Hence, opton B is correct.
 
2
ABCD is a cyclic trapezium such that AD || BC, if ∠ABC = 70°, then the value of ∠BCD is :
» Explain it
B

∠ABC + ∠CDA = 180°

∠CDA = 180° – ∠ABC = 180° – 70° = 110°

We know that,

∠BCD + ∠CDA = 180°

∴ ∠BCD = 180° – ∠CDA = 180° – 110° = 70°

Hence, opton B is correct.
 
3
If an exterior angle of a cyclic quadrilateral be 50°, then the interior opposite angles is :
» Explain it
C

∠ABC + ∠ADC = 180°

∠CBE = 50°

∴  ∠ABC = 180° – ∠CBE = 180° – 50° = 130°

∴  ∠ADC = 180° – ∠ABC = 180° – 130° = 50°

Hence, option C is correct.
 
4
ABCD is a cyclic quadrilateral and O is the centre of the circle. If ∠COD = 140° and ∠BAC = 40°, then the value of ∠BCD is equal to
» Explain it
A
The angle subtended at the centre by an arc is twice to that of angle subtended at the circumference.
 

∴  ∠CAD =  1  ∠COD = 70°
2

∴  ∠BAD = ∠BAC + ∠CAD = 70° + 40° = 110°

∴  ∠BCD = 180° – ∠BAD = 180° – 110° = 70°

Hence, option A is correct.
 
5
If the ratio of an external angle and an internal angle of a regular polygon is 1 : 17, then the number of sides of the regular polygon is
» Explain it
C

Let the number of sides of a regular polygon be n. Then,

According to question,

Exterior angle : Interior angle = 1 : 17
 

360°  :  ( 180° –  360° )  = 1 : 17
n n

 

360°  ×  n  =  1
n 180° (n – 2) 17


n – 2 = 34

n = 36

Hence, option C is correct.