Plz i'm doing a test and i need this answer to pass it.

use the diagarm to the left to answer the following
questions.
part a. using parallel line relationships to find the value of x.

part b. find the measure of each of the angles. label your answers.
a = d =
b = e =
c = f =

Step-by-step explanation:

Part A.

Angles with measures and are alternate interior angles when two parallel lines are cut by a transversal. By Alternate Interior Angles theorem,

Part B.

Angles a and are congruent as vertical angles, so

Angles and d are the same side interior angles, so the add up to 180°, thus

Angles d and f are congruent as vertical angles.

Angles e and are congruent as vertical angles.

Angles c and d are congruent as alternate interior angles.

Angles c and b are congruent as vertical angles.

Therefore,

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°

50-60=10

step-by-step explanation: