Naman is 4 times as old as his sister now. In 20 years’ time, Naman’s age will be 14
years less than twice his sister’s age. How old is Naman now?

Naman is 12 years old

Step-by-step explanation:

This means his sister is 3 which means in 20 years Naman will be 32 and his sister will be 23. Double 23 and you get 46 and 46 - 32 is 14

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°

answer: your correct answer is b. d.

step-by-step explanation: