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ABCD is a rectangle and its diagonals AC and BD intersect at O. If angle AOB = One hundred twenty °, find the measure of angle ABO, angle ADB and angle OCD.?
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ABCD is a rectangle and its diagonals AC and BD intersect at O. If ang...
In the given rectangle ABCD, we need to determine the measures of angles ABO, ADB, and OCD given that angle AOB = 120°.
Understanding the Geometry
- In a rectangle, the diagonals intersect each other at their midpoints and bisect each other.
- This means that triangle AOB is isosceles, as AO = BO (half of the diagonals).
Finding Angle ABO
- Since angle AOB = 120°, we can find angle ABO using the property of angles in a triangle.
- The sum of angles in triangle AOB is 180°:
- Angle AOB + Angle ABO + Angle OAB = 180°
- 120° + 2 * Angle ABO = 180°
- 2 * Angle ABO = 60°
- Angle ABO = 30°
Finding Angle ADB
- In triangle ADB, since AD is parallel to BC and AB is a transversal, angle ADB is equal to angle ABO.
- Therefore, Angle ADB = 30°
Finding Angle OCD
- Angle OCD is the angle opposite to angle AOB in triangle COD. Since diagonals bisect each other, angle AOB and angle OCD are equal.
- Therefore, Angle OCD = angle AOB = 120°
Final Measure of Angles
- Angle ABO = 30°
- Angle ADB = 30°
- Angle OCD = 120°
These relationships and calculations are derived from the properties of triangles and the geometric properties of rectangles.
Understanding the Geometry
- In a rectangle, the diagonals intersect each other at their midpoints and bisect each other.
- This means that triangle AOB is isosceles, as AO = BO (half of the diagonals).
Finding Angle ABO
- Since angle AOB = 120°, we can find angle ABO using the property of angles in a triangle.
- The sum of angles in triangle AOB is 180°:
- Angle AOB + Angle ABO + Angle OAB = 180°
- 120° + 2 * Angle ABO = 180°
- 2 * Angle ABO = 60°
- Angle ABO = 30°
Finding Angle ADB
- In triangle ADB, since AD is parallel to BC and AB is a transversal, angle ADB is equal to angle ABO.
- Therefore, Angle ADB = 30°
Finding Angle OCD
- Angle OCD is the angle opposite to angle AOB in triangle COD. Since diagonals bisect each other, angle AOB and angle OCD are equal.
- Therefore, Angle OCD = angle AOB = 120°
Final Measure of Angles
- Angle ABO = 30°
- Angle ADB = 30°
- Angle OCD = 120°
These relationships and calculations are derived from the properties of triangles and the geometric properties of rectangles.
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ABCD is a rectangle and its diagonals AC and BD intersect at O. If angle AOB = One hundred twenty °, find the measure of angle ABO, angle ADB and angle OCD.?
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ABCD is a rectangle and its diagonals AC and BD intersect at O. If angle AOB = One hundred twenty °, find the measure of angle ABO, angle ADB and angle OCD.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about ABCD is a rectangle and its diagonals AC and BD intersect at O. If angle AOB = One hundred twenty °, find the measure of angle ABO, angle ADB and angle OCD.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a rectangle and its diagonals AC and BD intersect at O. If angle AOB = One hundred twenty °, find the measure of angle ABO, angle ADB and angle OCD.?.
ABCD is a rectangle and its diagonals AC and BD intersect at O. If angle AOB = One hundred twenty °, find the measure of angle ABO, angle ADB and angle OCD.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about ABCD is a rectangle and its diagonals AC and BD intersect at O. If angle AOB = One hundred twenty °, find the measure of angle ABO, angle ADB and angle OCD.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a rectangle and its diagonals AC and BD intersect at O. If angle AOB = One hundred twenty °, find the measure of angle ABO, angle ADB and angle OCD.?.
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