A55 ft long drainage pipe must be cut into two pieces before installation. one piece is two-thirds as long as the other. find the length of each piece

33 feet

22 feet

Step-by-step explanation:

Let the longer piece be x

Therefore the shorter piece is (2/3)x

x + (2/3)x  = 55                  Combine the left 2 terms.

(3/3)x + (2/3)x = 55           Add  

(5/3)x = 55                        Multiply both sides by (3/5)

(3/5) * (5/3)x = (3/5)*55

x = 33

The larger piece is 33 feet

The smaller piece is (2/3) * 33 = 22 feet

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°

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