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 DCA and angle ACB.

Step 2. Apply an angle sum theorem.

Consider a right-angled triangle $DAC$, such that,

$$\begin{gathered} m\angle ADC+m\angle DAC+m\angle ACD=180 \\ 50+90+x=180 \\ x=40 \end{gathered}$$

Step 3. Description of step.

From figure it is clear that AB and CD are parallel lines. Therefore, two angles, CAB and DCA are alternate interior angles. Therefore, they are equal, that is, $m\angle CAB=40°$.

Step 4. Apply an angle sum theorem.

Consider a right-angled triangle ABC, such that,

$m\angle CAB+m\angle ABC+m\angle BCA=180$

$40+90+y=180$

$y=180-130$

$=50$

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