SOLUTION: The diagonal of rectangle ABCD intersect each other at O. If angle AOB = 30 degree, find angle COD and angle OCD.

Algebra.Com
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

RELATED QUESTIONS

In Rectangle ABCD angle cbd=35, diagonals intersect at o .how to find angle AOB? (answered by stanbon)
The diagonal of a rectangle PQRS intersect each other at O. if angle ROQ=40°, find the... (answered by Fombitz)
Line AOB is a straight line, angle AOC=5x, angle COD=(3x+30), and angle DOB=(2x+10). Find (answered by jim_thompson5910)
If Triangle AOB is congruent Triangle COD then Angle OAB is congruent to? angle ABO... (answered by nyc_function)
ABCD is a cyclic quadrilateral whose diagonals intersect at P such that angle DBC=30... (answered by Edwin McCravy)
find the area of a rectangle with diagonal 30 and with an angle 30 degree. (answered by robertb)
The diagonals of rectangle ABCD is 18 cm long and intersect in a 34 degree angle find the (answered by ikleyn)
In a circle O, AX and BY intersect at E. If angle BXY = 40°, angle YBX = 55°, and arc... (answered by greenestamps)