Question

Please help! Geometry!

Answer 1

Hello from MrBillDoesMath!

Answer:   x - 90, y = 43

Discussion:

The triangles are congruent by the SAS theorem. (In left triangle, side = AB, angle = y; other side = AD). Because of congruence,  angle ADC = x and (x + x = 180) as BDC is a straight line. So 2x = 180,or x = 90.

In the leftmost triangle : y + angle B +  angle x = 180 as the sum of all angles in a plane triangle is 180 degrees. But angle B = angle C  = 47 degrees as triangle  ABC is isosceles.  Putting this all together:

y + angle B +  angle x = 180  =>

y + 47 + x = 180  =>

y + 47 + 90 = 180  =>

y + 137 = 180 =>

y = 180 - 137 =  43

Thank you,

MrB