Question 1108289: The diagonal of rectangle ABCD intersect each other at O. If angle AOB = 30 degree, find angle COD and angle OCD.
Answer by PeanutTheCat(5)   (Show Source):
You can put this solution on YOUR website! 1. Angle COD and angle AOB are vertical angles. Vertical angles are congruent, so angle COD = 30 degrees.
2. Next, angle OCD is one of the base angles of an isosceles triangle formed within the rectangle. We know that it is an isosceles triangle because one of the properties of a rectangle is that diagonals are congruent. The diagonals also bisect each other because a rectangle is parallelogram, and that is a property of a parallelogram. We also know that the vertex angle, which happens to be angle COD, is 30 degrees.
3. Since the sum of the interior angles of a triangle = 180 degrees, and the base angles of an isosceles triangle are congruent, we can use this formula with x representing a base angle:
30 + 2x = 180
2x = 150
x = 75 degrees
So, angle OCD = 75 degrees
FINAL ANSWERS:
- Angle COD = 30 degrees
- Angle OCD = 75 degrees
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