Question

Find the m∠BAC, if m∠DEC= 45° and m∠EDC= 65°. AB || CD and BC || DE.50°70°60°80°

Answer 1

We the measures of ∠DEC and ∠EDC, which are internal angles in the triangle of the right. The sum of the measures of the 3 angles in a triangle is always equal to 180°. We can use that to calculate m∠DCE:

`m\angle\text{DCE}+m\angle\text{DEC}+m\angle\text{EDC}=180^o`

Replacing the measures we already know:

`m\angle\text{DCE}+45^o+65^o=180^o`

And solving:

`\begin{gathered} m\angle\text{DCE}=180^o-45^o-65^o \\ \\ m\angle\text{DCE}=70^o \end{gathered}`

Now we have found that m∠DCE is 70°.

As segments AB and CD are parallel, we can say that the angle they form with segment AE is the same. Then, we can simply say that:

`m\angle\text{DCE}=m\angle\text{BAC}`

Then, the measure of angle BAC is also 70°. The correct answer is the second option.