Question

May I please get help with problems (3), I have tried multiple times to find the correct answers for each of them but still could not get the accurate or at least correct answers

Answer 1

In an isosceles trapezoid, the base angles have the same measure pairwise.

The sum of the interior angles of a quadrilateral is 360º

For the given trapezoid:

`\begin{gathered} m\angle A+m\angle B+m\angle C+m\angle D=360 \\ \\ m\angle A=m\angle D \\ m\angle B=m\angle C \end{gathered}`

Given angle B has a measure of 110º

`m\angle B=m\angle C=110`
`\begin{gathered} 2m\angle A+2m\angle B=360 \\ \\ 2m\angle A+2(110)=360 \end{gathered}`

Use the equation above to find the measure of angle A:

`\begin{gathered} 2m\angle A+220=360 \\ 2m\angle A=360-220 \\ 2m\angle A=140 \\ m\angle A=(140)/(2) \\ \\ m\angle A=70 \\ \\ m\angle A=m\angle D=70 \end{gathered}`

Then, the measures of missing angles are:

`\begin{gathered} m\angle A=70 \\ m\angle C=110 \\ m\angle D=70 \end{gathered}`