Answer:
<E = 36 degrees (Answer B)
Step-by-step explanation:
Recall that the addition of all internal angles in a quadrilateral must equal 360 degrees. Then we can write the equation that states this as:
<E + <F + <G + <H = 360
Notice as well that we are dealing with an isosceles trapezoid, so there is a symmetry along the line that passes through the midpoints of sides FG and EH (the two bases). That means that the measures of angles <F = <G and <E = <H .
The previous equation then can be written as:
<H + <G + <G + <H = 360
Also, since we are told that <G = 4 <H, we can use this info in the equation as shown below:
<H + 4 <H + 4 <H + <H = 360
10 <H = 360
divide both sides by 10 to isolate <H
<H = 360 / 10
<H = 36
Since as we mentioned, <E equals <H, we can state that
the measure of <E = 36 degrees (Answer B)
