A woman came to a market to sell some eggs. A first buyer took half her eggs plus 1⁄2 an egg. The same happened with the remaining eggs: a second buyer took half her eggs plus 1⁄2 an egg. A third buyer took half of her remaining eggs plus 1⁄2 an egg. A fourth buyer took half of her remaining eggs plus 1⁄2 an egg. The woman then sold her last remaining egg to the fifth buyer. How many eggs were there initially if the woman never broke an egg? Show your steps.

since both sides equal, there are infinitely many olutions.

180

step-by-step explanation:

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°