Angles in a triangle may or may not be congruent.
The values of x and y are 90 and 47, respectively.
From the figure, we have:
\mathbf{AD \perp BC}AD⊥BC
This means that, angle x is a right-angle.
So, we have:
\mathbf{x = 90}x=90
Triangle ABC is an isosceles triangle.
So, we have:
\mathbf{\angle B = \angle C = 47}∠B=∠C=47
The measure of y is then calculated as:
\mathbf{y + \angle B + x = 180}y+∠B+x=180 --- sum of angles in a triangle
This gives
\mathbf{y + 47 + 90 = 180}y+47+90=180
\mathbf{y + 137 = 180}y+137=180
Subtract 137 from both sides
\mathbf{137 = 43}137=43
Hence, the values of x and y are 90 and 47, respectively.