Question

USE EFFICIENT METHODS Jim made a frame for a painting. He wants to check to make sure that opposite sides are parallel by measuring the angles at the corners and seeing whether they are right angles. How many corners must he check to be sure that the opposite sides are parallel?

Answer 1

two angles

Step-by-step explanation:

Let us assume that the frame of the painting is uneven. Then we'd have something like the following.

The above tells us that a four-sided figure can have arbitrary angle measures for as long as they add up to 360 degrees.

Therefore, to check whether the opposite sides are parrallel, we must check at most 2 angles to see if they are equal.

Let us say that the frame was unequal from all sides.

First what Jim would do is that he'd check angle 1 with angle 3. He'd find that they are not equal to 90 degrees. This means that no other angle pairs are equal and 90 degrees since such a combination would not add up to 360 degrees.

For example, if we have ∠1 = 100 and ∠3 = 120, then since

`\angle1+\angle2+\angle3+\angle4=360`
`100^o+\angle2+120^o+\angle4=360^o`
`220^o+\angle2+\angle4=360^o`
`\angle2+\angle4=140`

with means that if ∠2 = 90 then ∠4 = 50. In other words, ∠2 and ∠4 cannot be 90 degrees at the same time.