Question

(a) In each figure given below, ABCD is a rectangle. Find the value of x and y in each case.
(b) In the figure (i) prove that triangle ABCd is an isosceles triangle.​

Answer 1

Answer:

x=55° y=35°

Step-by-step explanation:

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 = 180o By substituting the values 110o + ∠ OAB + ∠ OBA = 180o We know that ∠ OAB = ∠ OBA So we get 2 ∠ OAB = 180o – 110o By subtraction 2 ∠ OAB = 70o By division ∠ OAB = 35o We know that AB || CD and AC is a transversal From the figure we know that ∠ DCA and ∠ CAB are alternate angles ∠ DCA = ∠ CAB = yo = 35o Consider △ ABC We know that ∠ ACB + ∠ CAB = 90o So we get ∠ ACB = 90o – ∠ CAB By substituting the values in above equation ∠ ACB = 90o – 35o By subtraction ∠ ACB = x = 55o Therefore, x = 55° and y = 35°