ACT Math assist » Geometry » plane Geometry » square » Trapezoids » how to uncover an edge in a trapezoid

Find the measure up of angle 

*
in the isosceles trapezoid pictured below.

You are watching: The sum of the measures of the angles of a trapezoid is:

 


*


*


*


*


Explanation:

The amount of the angle in any type of quadrilateral is 360°, and also the nature of an isosceles trapezoid dictate the the to adjust of angles adjoined by parallel lines (in this case, the bottom set and top set of angles) space equal. Subtracting 2(72°) indigenous 360° provides the amount of the two optimal angles, and dividing the resulting 216° through 2 yields the measure up of x, i m sorry is 108°.


Explanation:

As a rule, adjacent (non-paired) angle in a trapezoid room supplementary. Thus, we understand that if 

*
, then 
*
. Due to the fact that we are told that 
*
 and 
*
 are paired and also trapezoid 
*
 is isosceles, 
*
 must additionally equal 
*
.


Explanation:

To discover the measure up of edge DAC, we must know that the inner angles of all triangles sum up to 180 degrees. Also, together this is one isosceles trapezoid,

*
 and
*
 are equal to every other. The two diagonals within the trapezoid bisect angles
*
 and 
*
 at the very same angle.

Thus,

*
 must also be equal to 50 degrees.

Thus,

*
.

Now the we know two angles out the the 3 in the triangle top top the left, we have the right to subtract them indigenous 180 levels to uncover

*
:

*


Explanation:

All quadrilaterals" interior angles amount to 360°. In isosceles trapezoids, the two peak angles space equal to every other.

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

See more: What Does Thermal Energy Depend On, What Two Factors Does Thermal Energy Depend On

Therefore, to discover the amount of the 2 bottom angles, we subtract the actions of the peak two angles from 360:

*


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