ACT Math : How to find an angle in a quadrilateral
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Example Question #1 : How To Find An Angle In A Quadrilateral
A rectangle has two sets of parallel sides with all angles equaling 90 degrees.
Since 
Therefore 
Therefore
Example Question #431 : Plane Geometry
The rhombus above is bisected by two diagonals.
If 
Note: The shape above may not be drawn to scale.
A rhombus is a quadrilateral with two sets of parallel sides as well as equal opposite angles. Since the lines drawn inside the rhombus are diagonals, 
Therefore, 
Thus,
Since 
Example Question #3 : How To Find An Angle In A Quadrilateral
If 
Note: The figure may not be drawn to scale.
In a rhombus, opposite angles are equal to each other. Therefore we can set 
Therefore,
A rhombus, like any other quadrilateral, has a sum of angles of 360 degrees.
Example Question #4 : How To Find An Angle In A Quadrilateral
The interior angles of a quadrilateral are 
In order to solve this problem we need the following key piece of knowledge: the interior angles of a quadrilateral add up to 360 degrees. Now, we can write the following equation:
When we combine like terms, we get the following:
We will need to subtract 71 from both sides of the equation:
Now, we will divide both sides of the equation by 17.
We now have a value for the x-variable; however, the problem is not finished. The question asks for the measure of the smallest angle. We know that the smallest angle will be one of the following:
In order to find out, we will substitute 17 degrees for the x-variable.
Because 51 degrees is less than 71 degrees, the measure of the smallest angle is the following:
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