In the given figure, angle ABC is an equilateral triangle. If AB//CE, prove that angle ACE = angle ECD

Step-by-step explanation:

Triangle ABC is an equilateral triangle, then:

=> angle ABC = angle BAC = angle  ACB = 60 deg

AB // CE, according to alternative interior pair of angles theorem:

=> angle ACE = angle BAC = angle ABC = 60 deg   (1)

B, C, and D are colinear, then:

angle ECD + angle ACE + angle ACB = 180 deg

=> angle ECD = 180 - angle ACE - angle ACB = 180 - 60 - 60 = 60 deg   (2)

From (1) and (2):

=>angle ACE = angle ECD = 60 deg

3. (5x + 1) - (-10x + 6)

simplify the answer choice. combine like terms. remember to distribute the negative to the terms inside the second parenthesis. also remember that two negatives = one positive, and one of each sign = negative.

- (-10x + 6) = + 10x - 6

simplify. combine like terms:

5x + 1 + 10x - 6

5x + 10x + 1 - 6

15x - 5

∴ it is your answer

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