Test 21,753 for divisibility by 2, 3, 5, 9, and 10. 3 and 9

2, 3, and 9

3

2 and 9

21,753 is divisible by 3 and 9

Step-by-step explanation:

A number is  divisible by 2 if last digit of a number is 0, 2, 4 ,6 ,8

A number is  divisible by 3 if sum of digits is divisible by 3.

A number is  divisible by 5 if last digit of a number is 0 or 5

A number is  divisible by 9 if sum of digits is divisible by 9

A number is  divisible by 10 if last digit is 0.

So,  according to these rules  option (a) 3 ,9 is correct

Therefore , 21,753 is divisible by 3 and 9.          

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°