Point J is on line segment IK. Given JK = 2x, I J = 5x, and I K = x + 6, determine the numerical length of JK.
2

Step-by-step explanation:

JK = 2x, I J = 5x, and I K = x + 6,

|< x + 6 >|

IJK

          5x                        2x

x + 6 = 5x + 2x

6 = 7x - x

6 = 6x

x = 6 / 6

x = 1

substitute x=1 to JK

JK = 2x

    = 2(1)

     = 2

Answer -

JK = 2x, I J = 5x, and I K = x + 6,

x + 6 = 5x + 2x

6 = 6x

x = 6 / 6

x = 1

make the x=1 to JK

JK = 2x

   = 2(1)

    = 2

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°