1 In each of the figures given below ABCD is a rectangle Find the values of x and y in each case i...

Question

1 In each of the figures given below ABCD is a rectangle Find the values of x and y in each case i

Accepted Answer

i 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 By using the sum property of triangle AOB OAB OBA 180 By substituting the values we get AOB 35 35 180 On further calculation AOB 180 35 35 By subtraction AOB 180 70 AOB 110 From the figure we know that the vertically opposite angles are equal DOC AOB y 110 In ABC We know that ABC 90 Consider OBC We know that OBC x ABC OBA By substituting the values OBC 90 35 By subtraction OBC 55 Therefore x 55 and y 110 ii From the figure we know that the diagonals of a rectangle are equal and bisect each other Consider AOB We get OA OB We know that the base angles are equal OAB OBA By using the sum property of triangle AOB OAB OBA 180 By substituting the values 110 OAB OBA 180 We know that OAB OBA So we get 2 OAB 180 110 By subtraction 2 OAB 70 By division OAB 35 We know that AB CD and AC is a transversal From the figure we know that DCA and CAB are alternate angles DCA CAB y 35 Consider ABC We know that ACB CAB 90 So we get ACB 90 CAB By substituting the values in above equation ACB 90 35 By subtraction ACB x 55 Therefore x 55 and y 35

RS Aggarwal Solutions Class 9 Mathematics Solutions for Quadrilaterals Exercise 10B in Chapter 10 - Quadrilaterals