GRE Math help » Geometry » plane Geometry » quadrilaterals » Parallelograms » how to find an edge in a parallelogram

In a provided parallelogram, the measure up of among the inner angles is 25 levels less than another. What is the approximate measure up rounded to the nearest degree of the larger angle?


Explanation:

There space two contents to resolving this geometry puzzle. First, one have to be aware that the amount of the steps of the interior angles of a parallelogram is 360 levels (sum that the interior angles the a figure = 180(n-2), wherein n is the variety of sides that the figure). Second, one must understand that the various other two inner angles space doubles of those given here. For this reason if we assign one internal angle as x and also the various other as x-25, we uncover that x + x + (x-25) + (x-25) = 360. Combining favor terms leader to the equation 4x-50=360. Solving for x we uncover that x = 410/4, 102.5, or around 103 degrees. Since x is the measure up of the larger angle, this is our answer.

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Example inquiry #2 : just how To uncover An edge In A parallel


*

Figure 

*
 is a parallelogram.

Quantity A: The largest angle of 

*
.

Quantity B: 

*


Which the the adhering to is true?


Possible Answers:

Quantity B is larger.


Quantity A is larger.


The relationship cannot be determined.


The two quantities are equal.


Correct answer:

The two quantities are equal.


Explanation:

By making use of the nature of parallelograms along with those the supplementary angles, we have the right to rewrite our figure as follows:

*

Recall, for example, that angle 

*
 is equal to:

*
, hence 
*

Now, you understand that this angles deserve to all be included up to 

*
. Friend should also know that 
*

Therefore, you deserve to write:

*

Simplifying, girlfriend get:

*

*

*

Now, this way that:

*
 and 
*
. Thus, the 2 values are equal.

 


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Example concern #3 : exactly how To discover An angle In A parallel


*

Figure 

*
 is a parallelogram.


What is 

*
 in the figure above?


Possible Answers:

*


Cannot it is in computed from the data given.

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*



Correct answer:


Explanation:

Because of the personality of parallelograms, we recognize that our number can be redrawn as follows:

*

Because the is a four-sided figure, we understand that the sum of the angles should be 

*
. Thus, we know:

*

Solving for 

*
, we get:

*

*


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