Question

Find the values of x and y.

Answer 1

Remember that the angles of a triangle add up to 180 degrees.
Since lines AB and BC are equal in length, the angles opening toward them must be equal as well. Therefore, the following equation can be made:
\[x + y + 47 = 180\]
Which simplifies to:
\[x + y = 133\]

Answer 2

y=37,x=90

Answer 3

Now, hopefully x is a right angle, so that we can figure out the value of y.
We know that angles <BDA and <ADC are equal, since the lines they open towards are equal. We also know that lines BD and DC are equal, since the angles that point towards them are equal. x will only be a right angle if y is equal to angle <DAC, which is given, and lines BD and DC are equal, which we just proved.
So, x = 90 and the equation now looks like this:
\[y = 133 - 90\]