Question

PLEASE PLEASE HELP ASAPIn parallelogram ABCD, AD=19, EC=15, mABC=66°, mDAC=78° and mBDC=19°.Find mABD.

Answer 1

we can see that

We know that, in a parallelogram the opposite angles are equal to each other, this means that

`66=19+ADB`

hence, we have that

`\begin{gathered} \text{ADB}=66-19 \\ \text{ADB}=47 \end{gathered}`

Now, from the figure, we can see that, in the triangle ADB, we know angle ADB=47 and angle DAB=78.

Since all interior angles of a triangle add up 180, we have

`47+78+\text{ABD}=180`

and from this equality, we can find angle ABD. It yields

`\begin{gathered} 125+\text{ABD}=180 \\ \text{ABD}=180-125 \\ \text{ABD}=55 \end{gathered}`

hence, the answer is ABD=55 degrees