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Construction of Rectangle

If A B C D is...

Question

If ABCD is a rectangle with ∠BAC = 32°, find the measure of ∠DBC.

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Solution

Figure is given as :

Suppose the diagonals AC and BD intersect at O.

Since, diagonals of a rectangle are equal and they bisect each other.

Therefore, in , we have

Angles opposite to equal sides are equal.

Therefore,

But,

Now,

Hence, the measure of is .

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Similar questions

If $A B C D$ is a rectangle with $∠ B A C = 32^{\circ},$ find the measure of $∠ D B C .$

A B C D

is a rectangle with

∠ B A C = 48^{\circ}

∠ D B C

Q. ABCD is a rectangle with

∠ A B D = 40^{\circ}

∠ D B C + ∠ B A C

Q. Match List – I with List – II and select the correct answer using the codes given below the lists:

\begin{matrix} Properties & Quadrilaterals In a parallelogram ABCD If ∠ D = 115^{\circ},then the measure of ∠ A = & 68^{\circ} PQRS is a square such that PR and SQ intersect at O then the measure of ∠ P O Q = & 58^{\circ} The diagonals of a rectangle ABCD meet at O. If ∠ B O C = 44^{\circ}, then the measure of ∠ O A D = & 90^{\circ} If ABCD is a rectangle with ∠ B A C = 32^{\circ}, then the measure of ∠ D B C is = & 65^{\circ} \end{matrix}

Choose the correct option:

Q. Match List – I with List – II and select the correct answer using the codes given below the lists:

\begin{matrix} Properties & Quadrilaterals In a parallelogram ABCD If ∠ D = 115^{\circ},then the measure of ∠ A = & 68^{\circ} PQRS is a square such that PR and SQ intersect at O then the measure of ∠ P O Q = & 58^{\circ} The diagonals of a rectangle ABCD meet at O. If ∠ B O C = 44^{\circ}, then the measure of ∠ O A D = & 90^{\circ} If ABCD is a rectangle with ∠ B A C = 32^{\circ}, then the measure of ∠ D B C is = & 65^{\circ} \end{matrix}

Choose the correct option:

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