Question

2 numeric 1 point line ab is parallel to line de. what is the measure of ∠acd in degrees? answer

Explanation:

Step1: Find the measure of ∠BAC

Since the angle adjacent to the 115 - degree angle at point A is supplementary to it, ∠BAC=180 - 115 = 65 degrees.

Step2: Use the property of alternate - interior angles

Because AB is parallel to DE, ∠ABC and the angle at C (corresponding to ∠ABC) formed by the transversal are equal. Let's consider the triangle ABC. We know that the sum of angles in a triangle is 180 degrees. In triangle ABC, we want to find ∠ACB.
We know ∠BAC = 65 degrees and ∠ABC=35 degrees.

Step3: Calculate ∠ACB

Using the angle - sum property of a triangle (∠BAC+∠ABC + ∠ACB=180 degrees), we can find ∠ACB as 180-(65 + 35)=80 degrees.

Step4: Find ∠ACD

∠ACD and ∠ACB are supplementary. So ∠ACD = 180 - ∠ACB. Substituting the value of ∠ACB = 80 degrees, we get ∠ACD=100 degrees.

Answer:

100