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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