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# In triangle ABC, AC = BC, angle DCB is 40 degrees, and CD is parallel to AB. What is the number of degrees in angle ECD?

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In triangle ABC, AC = BC, angle DCB is 40 degrees, and CD is parallel to AB. What is the number of degrees in angle ECD?

#1
+7598
+2

∠DCB  and  ∠CBA  are alternate interior angles, so they have the same measure.

∠CBA  and  ∠BAC  are base angles of isosceles triangle ABC, so they have the same measure.

So..

m∠DCB   =   m∠CBA   =   m∠BAC   =   40°

And since there are  180°  in triangle  ABC,

m∠ACB   =   180° - 40° - 40°   =   100°

And...

m∠ACB  +  m∠DCB  +  m∠ECD   =   180°

100°  +  40°  +  m∠ECD   =   180°

m∠ECD   =   180°  -  40°  -  100°   =   40°

Feb 6, 2018

#1
+7598
+2

∠DCB  and  ∠CBA  are alternate interior angles, so they have the same measure.

∠CBA  and  ∠BAC  are base angles of isosceles triangle ABC, so they have the same measure.

So..

m∠DCB   =   m∠CBA   =   m∠BAC   =   40°

And since there are  180°  in triangle  ABC,

m∠ACB   =   180° - 40° - 40°   =   100°

And...

m∠ACB  +  m∠DCB  +  m∠ECD   =   180°

100°  +  40°  +  m∠ECD   =   180°

m∠ECD   =   180°  -  40°  -  100°   =   40°

hectictar Feb 6, 2018
#2
+1433
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Thanks so much! You're a life-saver!