Find the values of x and y x= 60 and y = 140 x= 60 and y = 40 x= 40 and y = 60 x= 120 and y = 140

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.

step-by-step explanation: