Q. 124.4( 10 Votes )

In each of the figures given below, is a rectangle. Find the values of and in each case.

(i) Here, ABCD is rectangle.

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

In AOB, we have OA = OB

This means that ∆ AOB is isosceles triangle.

We know that base angles of isosceles triangle are equal.

OAB = OBA = 35°

x = 90° − 35° = 55°

Also, AOB = 180° − (35° + 35°) = 110°

y = AOB = 110° Vertically opposite angles

Hence, x = 55° and y = 110°​​

(ii) Here, ABCD is rectangle.

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

In AOB, we have OA = OB

This means that ∆ AOB is isosceles triangle.

We know that base angles of isosceles triangle are equal.

OAB = OBA = × (180° − 110°) = 35°

y = BAC = 35° … alternate angles with transversal AC
Also, x = 90° – y
∵∠C = 90° = x + y
x = 90° − 35° = 55°
Hence, x = 55° and y = 35°
​​

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