Question

Triangles ACD and BCD are isosceles. Angle DBC has a measure of 84 degrees and angleBDA has a measure of 24 degrees. Find the measure of angle BAC.

Answer 1

The Solution.

The reflex angle DBC can be calculated as below:

$\angle DBC=360-84=276^o\text{ ( angle at a point)}$$So,\text{ }\angle DBA=\angle CBA=\frac{276}{2}=138^o$

Note that: angle BDA = angle BCA = 24 degrees

Thus, considering triangle CBA (which is similar to triangle DBA), we can find angle BAC.

$\angle BAC+138+24=180\text{ (sum of angles in a triangle)}$$\begin{gathered} \angle BAC=180-(138+24) \\ \text{ =180-162} \\ \text{ =18 }^o \end{gathered}$

Therefore, the correct answer is 18 degrees.