In the figure given below, ABCD is a rectangle. Find the values of x

1.	In the figure given below, ABCD is a rectangle. Find the values of x and y.
Answer» From the figure we know that the diagonals are equal and bisect at point O. Consider △ AOB We get AO = OB We know that the base angles are equal ∠ OAB = ∠ OBA = 35^o By using the sum property of triangle ∠ AOB + ∠ OAB + ∠ OBA = 180^o By substituting the values we get ∠ AOB + 35^o+ 35^o= 180^o On further calculation ∠ AOB = 180^o – 35^o– 35^o By subtraction ∠ AOB = 180^o – 70^o ∠ AOB = 110^o From the figure we know that the vertically opposite angles are equal ∠ DOC = ∠ AOB = y = 110^o In △ ABC We know that ∠ ABC = 90^o Consider △ OBC We know that ∠ OBC = x^o = ∠ ABC – ∠ OBA By substituting the values ∠ OBC = 90^o – 35^o By subtraction ∠ OBC = 55^o Therefore, x = 55^o and y = 110^o.

In the figure given below, ABCD is a rectangle. Find the values of x and y.

Answer»

From the figure we know that the diagonals are equal and bisect at point O.

Consider △ AOB

We get AO = OB

We know that the base angles are equal

∠ OAB = ∠ OBA = 35^o

By using the sum property of triangle

∠ AOB + ∠ OAB + ∠ OBA = 180^o

By substituting the values we get

∠ AOB + 35^o+ 35^o= 180^o

On further calculation

∠ AOB = 180^o – 35^o– 35^o

By subtraction

∠ AOB = 180^o – 70^o

∠ AOB = 110^o

From the figure we know that the vertically opposite angles are equal

∠ DOC = ∠ AOB = y = 110^o

In △ ABC

We know that ∠ ABC = 90^o

Consider △ OBC

We know that

∠ OBC = x^o = ∠ ABC – ∠ OBA

By substituting the values

∠ OBC = 90^o – 35^o

By subtraction

∠ OBC = 55^o

Therefore, x = 55^o and y = 110^o.

Discussion

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