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In a offered parallelogram, the measure up of one of the interior angles is 25 degrees less than another. What is the approximate measure up rounded to the nearest level of the bigger angle?


Explanation:

There room two contents to solving this geometry puzzle. First, one must be conscious that the amount of the actions of the inner angles of a parallelogram is 360 degrees (sum of the internal angles of a number = 180(n-2), wherein n is the variety of sides of the figure). Second, one must know that the other two internal angles are doubles of those provided here. Therefore if we assign one inner angle as x and also the other as x-25, we discover that x + x + (x-25) + (x-25) = 360. Combining choose terms leader to the equation 4x-50=360. Resolving for x we discover that x = 410/4, 102.5, or roughly 103 degrees. Because x is the measure up of the bigger angle, this is our answer.

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Example concern #2 : just how To discover An edge In A parallelogram


*

Figure 

*
 is a parallelogram.

Quantity A: The largest angle of 

*
.

Quantity B: 

*


Which that the following is true?


Possible Answers:

Quantity B is larger.


The two amounts are equal.


The relationship cannot it is in determined.


Quantity A is larger.


Correct answer:

The two quantities are equal.


Explanation:

By utilizing the properties of parallelograms along with those the supplementary angles, we have the right to rewrite our number as follows:

*

Recall, because that example, the angle 

*
 is same to:

*
, hence 
*

Now, you recognize that these angles deserve to all be added up to 

*
. Girlfriend should also know that 
*

Therefore, you have the right to write:

*

Simplifying, you get:

*

*

*

Now, this way that:

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

 


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Example question #3 : exactly how To uncover An angle In A parallel


*

Figure 

*
 is a parallelogram.


What is 

*
 in the figure above?


Possible Answers:

*



*


Cannot it is in computed indigenous the data given.

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Correct answer:


Explanation:

Because of the personality of parallelograms, we know that our figure can it is in redrawn as follows:

*

Because the is a four-sided figure, we understand that the amount of the angles have to be 

*
. Thus, us know:

*

Solving for 

*
, us get:

*

*


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