Question

50 Points, Will mark brainliest!
Identify the theorem or postulate that is related to the measures of the angles in the pair, and find the unknown angle measures.

m∠ACD=(5x+25)∘, m∠BDC=(25x+35)∘

Answer 1

Answer:

m∠ACD = 50°

m∠BDC = 160°

Step-by-step explanation:

From the picture attached,

Two parallel lines AC and BD are intersected by a transversal line.

Angles formed ∠ACD and ∠BDC are the consecutive angles.

By the theorem of consecutive interior angles,

m∠ACD + m∠BDC = 180°

(5x + 25)° + (25x + 35)° = 180°

30x + 60 = 180

30x = 180 - 60

30x = 150

x = 5

Therefore, m∠ACD = (5x + 25)

                                 = 5(5) + 25

                                 = 50°

And m∠BDC = (25x + 35)°

                      = 25(5) + 35

                      = 125 + 35

                      = 160°