8. A carpenter cut the top section of a window frame with a 37 degree angle on each end. The side pieces each have 50 degree angle cut at their top ends, as shown. Will the side pieces of the frame be parallel? Explain

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Mathematics

Bryant Martinez

16 July, 00:04

8. A carpenter cut the top section of a window frame with a 37 degree angle on each end. The side pieces each have 50 degree angle cut at their top ends, as shown. Will the side pieces of the frame be parallel? Explain

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Marvin Robinson · Answer 1

I will assume that the end of the top section if it were cut at 0 degrees would be cut at right angles to the length of the section.

Joining a top section with a 37 degree end angle to a side piece with a 50 degree end angle will result in the length of the side piece being at an angle of

37 + 50 = 87 degrees to each other.

The same will be true for the other side.

If the sides were parallel, then going up one side, across the top and then down the other side will result in a change of direction of 180 degrees. However, in this frame the direction turns 87 degrees at the first top corner and another 87 degrees at the second top corner. This is a total of

87 + 87 = 174 degrees instead of 180 degrees.

The two sides diverge at an angle of

180 - 174 = 6 degrees from each other as they extend downwards from the top of the frame