What is the value of x and the length of segment DE? StartFraction 5 Over 9 EndFraction = StartFraction 9 Over 2 x + 3 EndFraction
10x + 15 = 9(9)

x = _
Length of = ___units

Step-by-step explanation:

This is a geometric means problem involving the height of 9. 9 is the geometric mean because it is the height of both ΔCFD and ΔEFD. Set up the problem accordingly:

and cross multiply:

81 = 5(2x + 3) and

81 = 10x + 15 and

66 = 10x so

x = 6.6

Now we will plug that value in for x to find the length of DE:

2(6.6) + 3 = 16.2 units

351.23

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°