Question

The diagonal of rectangle ABCD intersect in O if angle BOC is 70
find angle ODA

Answer 1

Answer:

Step-by-step explanation:

angle ODA=55° because when diagonal bisect each other then it former isosceles triangle and one angle is given as 7D show the sides opposite to equal angles are equal in the isosceles Triangles show by angle sum property the angle b c o is equal to 55 degree and the sides are parallel in the rectangle so opposite angle o d a is equal to 55 degree

Answer 2

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Questions & Answers

CBSE

Mathematics

Grade 9

Geometry

Question

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Related Questions

The diagonals of a rectangle ABCD intersect at O, if ∠BOC=70∘

. Find ∠ODA

Answer

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Hint:

Here, we have to find the measure of a given angle. We will use the properties of angles in a rectangle and triangle. We will first find the measure of the opposite angle of the given angle using the property vertically opposite angle. Then we will use the property of isosceles triangle and sum property of a triangle to find the measure of the required angle.

Complete step by step solution:

Let ABCD be a rectangle. The diagonals of a rectangle ABCD intersect at O.

We are given that ∠BOC=70∘

.

We know that in a rectangle, vertically opposite angles are equal.

By using this property, we get

∠BOC=70∘=∠AOD

………………………………………………………………………….(1)

We know that the diagonals of a rectangle are equal and bisect each other.

So, in ΔAOD

, we get

AO=OD

We know that angles opposite to equal sides of an isosceles triangle are equal.

By using this property, we get

∠OAD=∠ODA

……………………………………………………………………………………………(2)