Calculate Angle ABC in Parallelogram with Given Angles 40° and 44°

Look at the parallelogram below and calculate the size of angle ABC ∢\text{ABC} .

AAABBBCCCDDD4044

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Step-by-step video solution

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00:00 Calculate angle ABC
00:08 Alternate angles are equal between parallel lines
00:20 The angle equals the sum of its parts
00:25 Therefore, let's sum up the angles to get the angle itself
00:29 Let's substitute appropriate values and solve
00:45 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Look at the parallelogram below and calculate the size of angle ABC ∢\text{ABC} .

AAABBBCCCDDD4044

2

Step-by-step solution

Since we are dealing with a parallelogram, there are 2 pairs of parallel lines.

As a result, we know that angle ADB and angle DBC are alternate angles between parallel lines and therefore both are equal to each other (44 degrees):

ADB=DBC=44 ADB=DBC=44

Now we can calculate angle ABC as follows:

ABC=ABD+DBC ABC=ABD+DBC

Finally, let's substitute in our values:

ABC=40+44=84 ABC=40+44=84

3

Final Answer

84

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If one of two corresponding angles is a right angle, then the other angle will also be a right angle.

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