Question

You are given an isosceles trapezoid ABCD with median XY. Complete the following.m

Answer 1

The measure of m<BAD is equivalent to 70 degrees

The given diagram is a trapezium with the following given angle

m<ABC = 110 degrees

We are to determine the measure of angle m<BAD

Since the sum of adjacent angles is 180 degrees to have:

m<ABC + m<BAD = 180

110 + m<BAD = 180

m<BAD = 180 - 110

m<BAD = 70 degrees

Hence the measure of m<BAD is equivalent to 70 degrees

Answer 2

From the statement, we know that:

`m\angle ABC=110^(\circ)\text{.}`

If we extend the segments AD and BC, we have:

From the picture, we see that:

1) The angle m∠SBA is the complement angle of m∠ABC, so we have:

`\begin{gathered} m\angle\text{SBA + m}\angle ABC=180^(\circ), \\ m\angle\text{SBA }=180^(\circ)-\text{ m }\angle ABC, \\ m\angle\text{SBA = }180^(\circ)-110^(\circ)=70^(\circ). \end{gathered}`

2) m∠SBA and m∠WAZ are congruent angles, so we have:

`m\angle WAZ=m\angle SBA=70^(\circ)\text{.}`

3) Finally because m∠WAZ and m∠BAD are opposite angles, they must be equal:

`m\angle\text{BAD}=70^(\circ)\text{.}`

Answer

m∠BAD = 70°