Lines p and q are cut by a transversal. At the intersection of line p with the transversal, the bottom right angle is x. At the intersection of line q with the transversal, the bottom left angle is y and the bottom right angle is z. Letters x, y, and z are angle measures. Which equations would guarantee that lines p and q are parallel? Check all that apply. x = z x + y = 180° x + z = 180° x = y z = 180°

x = z  

x + y = 180°

Explanation: Just did it on Edgenuity.

x = z and x + y  =  180

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°