In parallelogram ABCD m

Question

In parallelogram ABCD m<abd=83,m<bda=34, m<bcd=__

cashgirl1369 · Answer

attachment

cashgirl1369 · Answer

pleaes help me

mathstudent55 · Answer

What is the sum of the measures of the angles of a quadrilateral?

cashgirl1369 · Answer

i have 114

mathstudent55 · Answer

Is that the answer to the problem, or the answer to my question?

cashgirl1369 · Answer

i dont know

mathstudent55 · Answer

You wrote "I have 114."
Where did that come from?

cashgirl1369 · Answer

i added the two langles i have together

mathstudent55 · Answer

Is 83 + 34 = 114?

cashgirl1369 · Answer

yes

mathstudent55 · Answer

Ok, let's do this.
I asked a question above, not to bother you, but because it is part of the solution of the  problem.
There are several things you need to know to solve this problem.

mathstudent55 · Answer

1. The sum of the measures of the angles of a polygon is 

180(n - 2)

where n = number of sides.

mathstudent55 · Answer

In your case, you have a parallelogram.
A parallelogram has 4 sides, so n = 4.
We use the formula with n = 4:

180(n - 2) = 180(4 - 2) = 180(2) = 360

The sum of the measures of the angles of a parallelogram is 360.

Ok so far?

cashgirl1369 · Answer

okay i kinda understand that

mathstudent55 · Answer

2. Another thing you need for this problem.
In a parallelogram, opposite angles are congruent.
Remember congruent angles are angles that have the same measure.

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mathstudent55 · Answer

Look at the figure above.
Quadrilateral ABCD is a a parallelogram.
Since angle A measures 120 deg, then the opposite angle, and C must also measure 120 deg.

Ok so far?

cashgirl1369 · Answer

ok

mathstudent55 · Answer

Since opposite angles are congruent, angles A and C are congruent and have the same measure.
If angle A measures 120 deg, then angle C also measures 120 deg.
This allows us to find the measures of angles B and D.

Angles B and D are opposite angles in a parallelogram, so they have the same measure.
Since all angles of a parallelogram add up to 360 degrees, subtract 120 for angle A and 120 for angle C, and you have 360 - 120 -120 = 120.
Angles B and D add up to 120 deg and have the same measure, so angles B and D both measure 60 degrees.

mathstudent55 · Answer

This means that once you know the measure of one angle of a parallelogram, you can find the measures of the other three angles.

cashgirl1369 · Answer

okay i understand that but how did you find the 3 one

mathstudent55 · Answer

3. You need to use alternate interior angles of parallel lines.

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cashgirl1369 · Answer

i get that

mathstudent55 · Answer

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cashgirl1369 · Answer

x would be 34

mathstudent55 · Answer

Sides BC and AD are parallel.
That is part of the definition of a parallelogram.
What is the measure of angle x? (Hint: use alternate interior angles.)

mathstudent55 · Answer

Wow, you answer before I ask.

mathstudent55 · Answer

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cashgirl1369 · Answer

i kinda figured you would ask

cashgirl1369 · Answer

i just cant see how you get the other one

mathstudent55 · Answer

Now that we know that that angle above is 34, we add 34 and 83 to get the measure of the entire angle of the parallelogram.
What is 83 + 34? (Hint: it is not 114.)
(Notice the last digits 3 and 4 add to 7 not to 4.)

cashgirl1369 · Answer

117

mathstudent55 · Answer

Much better.
Now this is the problem we have.
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