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Two opposite angles of a parallelogram are (5x – 8)° and (2x + 82)°. Find the measures of each angle of the parallelogram.

User Li Jinyao
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1 Answer

3 votes

Answer:

2 angles are 142 degrees

2 angles are 38 degrees

Explanation:

In any parallelogram, the opposite angles are congruent.

So,

5x - 8 = 2x + 82

3x - 8 = 82

3x = 90

x = 30

Now lets plug in x into one of the angles:

5 ( 30 ) - 8

150-8

142

So, because that angle is 142, the other angle must also be 142. However, to make sure, we should still check.

2 ( 30 ) + 82

60 +82

142

As we can see, both angles are 142.

Now we have figured out 2 angles, and they are both 142. Now lets figure out the other 2 angles.

Any 4 sided shape has 360 degrees

142 + 142 = 284 degrees

Our 2 angles have 284 degrees in total.

if we subtract 284 from 360, we get 76.

Our remaining 2 angles have a total of 76 degrees. Because these angles are also opposite, we must divide by 2. 76/2 is 38.

So,

2 angles are 142 degrees

2 angles are 38 degrees

User Psanf
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