The area of a rectangle is 34in² the length is 13 less than 2 times the width

  width:  8.5

  length:  4

Step-by-step explanation:

width:  x

length:  2x - 13

area = length * width

34 = (2x - 13)x

34 = 2x² - 13x

2x² - 13x - 34 = 0

(2x - 17)(x + 2) = 0

2x - 17 = 0

 2x = 17

  x = 8.5

x + 2 = 0

    x = -2              width cannot be negative so discard this

width:  x = 8.5

length:  2x - 13 = 2(8.5) - 13 = 4

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°