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# Isosceles Triangles and Triangle Sum Theorem

ACTMAT-JKT4IM

Triangle ABC is an isosceles triangle with vertex A and $AB = AC.$ Points D and E are placed on segments AB and AC, respectively, so that $CD = DE = AE.$ Refer to the figure below.

If the $m{\angle }A = x$, what is $m{\angle }BCD$ (in degrees) in terms of $x$?

A

${\cfrac { 1 }{ 2 } x}$

B

$x$

C

$90-{\cfrac { 1 }{ 2 } x}$

D

$90-{\cfrac { 5 }{ 2 } x}$

E

$90-{\cfrac { 7 }{ 2 } x}$