Find the coordinates of the missing endpoint if M
is the midpoint of AB.
A(4, -8) and M(5,-2)

  B = (6, 4)

Step-by-step explanation:

You know that the midpoint is calculated as ...

  M = (A +B)/2

Solving this for B, we find ...

  2M = A + B

  B = 2M - A

Filling in the coordinate values, we get ...

  B = 2(5, -2) -(4, -8) = (2·5-4, 2(-2)+8)

  B = (6, 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°