Q In figure given below, ABCD is a rectangle and diagonals intersect at O AC is produced to - Maths - Rectilinear Figures

Question

Q In figure given below, ABCD is a rectangle and diagonals
intersect at O AC is produced to E If ∠ ECD = 146 ° ,
find the angles of triangle AOB

Manbar Singh · Accepted Answer

∠OCD + ∠ECD = 180°   Linear pair⇒∠OCD + 146° = 180°⇒∠OCD = 34°Now, ABCD is a rectangle
So, AB∥CD and AD∥BC
Since, AB∥DC  and AC is a transversal, then∠OAB = ∠OCD   Alternate interior angles⇒∠OAB = 34°Now, diagonals of a rectangle are equal
So, AC = BD⇒12AC = 12BD⇒OA = OB   Since, diagonals of a rectangle bisect each other⇒∠OBA = ∠OAB   Angles opposite to equal sides are equal⇒∠OBA = 34°In ∆AOB,∠AOB + ∠OAB + ∠OBA = 180°  Angle sum property⇒∠AOB + 34° + 34° = 180°⇒∠AOB + 68° = 180°⇒∠AOB = 112°

Q. In figure given below, ABCD is a rectangle and diagonals intersect at O. AC is produced to E. If ∠ ECD = 146 ° , find the angles of triangle AOB.

Q. In figure given below, ABCD is a rectangle and diagonals intersect at O. AC is produced to E. If $∠$ ECD = 146 $°$ , find the angles of triangle AOB.