Question

I need a bit of help understanding this, please help

Answer 1

We know that

`\begin{gathered} m\angle DAC=87^(\circ) \\ \text{ And} \\ m\angle ACD=43^(\circ) \end{gathered}`

And we must find the measure of angle B

We can see the lines AB and DC are crossed by a transversal

We can see that blue angles are alternate interior angles, so

`\begin{gathered} m\angle ACD=m\angle ACB \\ \text{ Then,} \\ m\angle CAB=43^(\circ) \end{gathered}`

And knowing that lines AD and BC are parallels we can say that

`\begin{gathered} m\angle DAC=m\angle ACB \\ \text{ Then,} \\ m\angle ACB=87^(\circ) \end{gathered}`

Finally, using that the three interior angles of a triangle always add to 180° we can say that

`\begin{gathered} m\angle ABC+m\angle ACB+m\angle CAB=180^(\circ) \\ \text{ Replacing the values of the angles} \\ m\angle ABC=180^(\circ)-(87^(\circ)+43^(\circ)) \\ m\angle ABC=50^(\circ) \end{gathered}`

ANSWER:

The measure of angle B is 50°