Three consecutive integers have a sum of 15. what are the integers?

4, 5, 6

Step-by-step explanation:

First integer is X, consecutive is (x+1), next consecutive is (X+1+1)=(X+2)

Three consecutive integers have a sum of 15. X+X+1+X+2 = 15

X+X+1+X+2 = 15

3X + 3 = 15

3X = 15-3

3X = 12

X = 4

X+1 = 4+1=5

X+2 = 4+2=6

Check: 4+5+6=15, 15=15

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°