SOLUTION: In the diagram, ABCD is a square. Find angle ECD in degrees. (E is the center of the square.)

Click here to see ALL problems on Length-and-distance

Question 1210682: In the diagram, ABCD is a square. Find angle ECD in degrees.
(E is the center of the square.)
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(53996) (Show Source):
You can put this solution on YOUR website!
.

Angle ECD is 45 degrees, which is absolutely obvious.

For the proof, use this reasoning.

Since ABCD is a square, it is a rhombus, in particular.
Each diagonal of a rhombus divides the interior angle of a rhombus in half.

Answer by math_tutor2020(3844) (Show Source):
You can put this solution on YOUR website!

Answer: 45 degrees

Reason:
Form segment AC to determine that triangle ADC is congruent to triangle ABC.
Use the SSS (side side side) congruence theorem.

Because of this triangle congruence, we know that angle ECB = angle ECD. They are corresponding angles.
This means angle BCD has been bisected to form angles ECB and ECD.

Each interior angle of a square is 90 degrees.
Therefore, angle ECD = (angle BCD)/2 = 90/2 = 45.