Question

1. Quadrilateral EFGH is an isosceles trapezoid. If mG is four times mH, what is mE? A)18° C)72° D)144° B)36°​

Answer 1

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)