ACT Math help » Geometry » plane Geometry » quadrilaterals » Trapezoids » just how to discover an edge in a trapezoid

Find the measure up of angle 

*
in the isosceles trapezoid pictured below.

You are watching: What is the sum of the angles in a trapezoid

 


*


*


*


*


Explanation:

The amount of the angles in any type of quadrilateral is 360°, and also the nature of one isosceles trapezoid dictate the the set of angles adjoined by parallel currently (in this case, the bottom collection and top set of angles) are equal. Individually 2(72°) indigenous 360° gives the sum of the two top angles, and dividing the resulting 216° by 2 yields the measure up of x, which is 108°.


Explanation:

As a rule, surrounding (non-paired) angles in a trapezoid space supplementary. Thus, we recognize that if 

*
, then 
*
. Because we are told that 
*
 and 
*
 are paired and also trapezoid 
*
 is isosceles, 
*
 must likewise equal 
*
.


Explanation:

To find the measure of edge DAC, we must recognize that the interior angles of every triangles amount up to 180 degrees. Also, as this is an isosceles trapezoid,

*
 and
*
 are equal to each other. The 2 diagonals within the trapezoid bisect angle
*
 and 
*
 at the exact same angle.

Thus,

*
 must also be same to 50 degrees.

Thus,

*
.

Now that we know two angle out that the three in the triangle on the left, we deserve to subtract them native 180 levels to uncover

*
:

*


Explanation:

All quadrilaterals" internal angles sum to 360°. In isosceles trapezoids, the two peak angles room equal to every other.

Similarly, the two bottom angles room equal to each various other as well.

Therefore, to find the sum of the 2 bottom angles, us subtract the procedures of the top two angles from 360:

*


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