Question

Find the values of x and y.

Short answer

The values of x and y are $40°$and$50°$ respectively.

Step-by-step solution

Step 1. Name the figure and highlight angle ACF and angle FAC.

Step 2. Apply an angle sum theorem.

Consider a right-angled $\Delta BDC$, such that,

$$\begin{gathered} m\angle BDC+m\angle DCB+m\angle CBD=180 \\ 90+y+40=180 \\ y=50 \end{gathered}$$

Step 3. Apply an angle sum theorem.

Consider a right-angled $\Delta AFC$, such that,

$$\begin{gathered} m\angle AFC+m\angle ACF+m\angle FAC=180 \\ 90+50+x=180 \\ x=40 \end{gathered}$$

Therefore, the values of x and y are $40°$and $50°$respectively.