The sum of the measures of the interior angles of the parallelogram is 360°. Write and solve an equation to find the value of each of the unknown angles.

Answer 1

Look at the image for reference

https://www.mathplanet.com/Oldsite/media/44000/parallelogram_499x300.jpg

Angle A = C

And angle D =B

It's difficult to explain how this is true without going into some geometry and proofs, but just look at the picture to see if you can make sense of why this is true.

And we also know that if you sum up all the angles, you get 360 degrees

Also, since A=C and D=B, we can just say that 2A accounts for both angles A and C

and 2D accounts for angles D and B. All I'm doing is saying, since A=C, I'll just combine the two to make 2A (or it could have been 2B), and D=B is now 2D

One equation we could write then is

2A+2D=360

Divide both sides by 2

A + D = 180

A and D can be many different answers (infinitely many?)

A=90

D=90

or

A=45

D=135

or

A=179

D=1

It doesn't matter as long as A and D add to make 180.

We can make up a problem to see if the equation works. Let's say angle A =25, what are angles B, C, and D when the total is 360?

2(A) +2(D) =360

2(25) +2(D)=360

50+ 2(D) =360

2D=310

D= 155

So this means that

A=25

and

D=155

And A=C

D=B so

A=25

C=25

D=155

B=155

Just make sure all 4 angles add up to 360

25+25+155+155 =360 !!!

This is difficult to explain without a visual aid, but I hope it helped a little. Good luck.