ACT Math aid » Geometry » aircraft Geometry » quadrilaterals » Parallelograms » exactly how to discover an angle in a parallel

*

In parallelogram 

*
*
 and the elevation is 
*
. What is 
*
?


*


*


*


*


Explanation:

We can start this problem by illustration the height and labeling the lengths with the offered values.

You are watching: Consecutive angles in a parallelogram are

*

When we carry out this, we have the right to see that us have attracted a triangle inside the paralellogram including 

*
. Due to the fact that we know the lengths of two sides that this triangle, we have the right to use trigonometry come find 
*
.

With respect to 

*
, we understand the values of the opposite and also hypotenuse political parties of the triangle. Thus, we deserve to use the sine duty to deal with for 
*
.

*

*

*


Explanation:

In a parallelogram, consecutive angles are supplementary (i.e. Include to 

*
) and also opposite angles room congruent (i.e. Equal). Making use of these properties, we have the right to write a mechanism of equations.

1. 

*

2. 

*

 

Starting through equation 1.,

*

*

*

 

Now substituting into equation 2.,

*

*

*

*

*

 

Finally, since opposite angles are congruent, we recognize that 

*
.

*

*


Explanation:

In a parallelogram, continuous angles room supplementary and opposite angles are congruent. Utilizing these properties, we deserve to write a system of equations.

1. 

*

2. 

*

3. 

*

 

Starting with equation 1.,

*

*

*

 

Substituting into equation 2.,

*

*

*

*

 

Using equation 3.,

*

*


Explanation:

In a parallelogram, continuous angles space supplementary and opposite angles room congruent.

*

*

*

*

*

 

*

*

*


Explanation:

In the above parallelogram, 

*
 and 
*
 are consecutive angle (i.e. Next to each other). In a parallelogram, consecutive angle are supplementary, an interpretation they add to 
*
.

*

*

*


Explanation:

In parallelogram 

*
*
 and 
*
 are the contrary angles. In a parallelogram, the contrary angles are congruent. This way these two angles are equal.

*

*


Explanation:

In a parallelogram, continually angles space supplementary.

*
 and 
*
 are consecutive, so their amount is 
*
.


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