Question

In the given figure, find the angle measure x.

Answer 1

Sum of all the interior angles of an n-sided polygon = $\left(n-2\right)\times 180°$

$$\begin{gathered} m\angle ADC=180-50={130}^o \\ m\angle DAB=180-115={65}^o \\ m\angle BCD=180-90={90}^o \\ m\angle ADC+m\angle DAB+m\angle BCD+m\angle ABC=\left(n-2\right)\times 180°=(4-2)\times 180°=2\times 180°=360° \\ \Rightarrow m\angle ADC+m\angle DAB+m\angle BCD+m\angle ABC=360° \\ \Rightarrow {130}^o+{65}^o+{90}^o+m\angle ABC=360° \\ \Rightarrow {285}^o+m\angle ABC={360}^o \\ \Rightarrow m\angle ABC={75}^o \\ \Rightarrow m\angle CBF=180-75={105}^o \end{gathered}$$
∴ x = 105