Wayne exercised for 5/6 of an hour in the morning and 1/3 of an hour in the evening. How much more of an hour did Wayne spend exercising in the morning than in the evening?

of an hour

Step-by-step explanation:

Given:

Wayne exercised for 5/6 of an hour in the morning and 1/3 of an hour in the evening

To find:

Additional hours spent by Wayne exercising in the morning than in the evening.

Solution:

Time spent by Wayne in the morning = of an hour

Time spent by Wayne in the evening = of an hour = of an hour

So, Wayne spends more in the morning than in the evening.

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°

true

step-by-step explanation: