Question

In the given figure, ABCD is a rectangle, diagonals AC and BD intersect at O and angle AOB=60degree Find the measure of angle oad

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Answer 1

Answer:

Angle OAD= 30°

Step-by-step explanation:

Consider giving 'Branliest' if I could give a nice answer.

Given,

ABCD is a Rectangle whose respective diagonals are AC & BD.

We know, the diagonals of a Rectangle are of equal size.

Therefore,

• AC=BD
• 1/2AC =1/2 BD
• AO=CO = BO=DO [Since, both the diagonals intersect each other at the center and, AC= AO+CO & BD= BO+DO]

• AO=BO [Since, AO=CO=BO=DO]

We know, the opposite angles of 2 equal sides of a triangle are equal. And, summation of all the angles of a triangle is equals 180°.

A/Q,

Angle AOB = 60°

Angle BAO+Angle ABO+Angle AOB=180°

Angle BAO+Angle ABO+60°= 180°

Angle BAO+Angle ABO= 180° - 60°

Angle BAO+Angle ABO= 120°

Angle BAO+Angle BAO= 120°

[Since Angle BAO = Angle ABO]

2 x Angle BAO= 120°

Angle BAO= 120° ÷ 2

Angle BAO= 60°

Again, all the corners of a triangle are Right Angles.

Therefore,

• Angle BAD= 90°
• Angle BAO + Angle OAD= 90°
• 60° + Angle OAD= 90°
• Angle OAD= 90° - 60°
• Angle OAD= 30°