Question

The diagonals of a rhombus ABCD intersect at the point O. If BDC = 50°, then OAB = ?

Answer 1

Its given ABCD is a prallagram and AC and BD are its diagonals interesecting at point O .

Given :

angle BOC = 900

angle BDC = 500

To find : angle OAB

i) angle BOC= 180° ( linear pair )

angle COD 180 ° - angle BOC

COD 180° - 90° COD = 90 °

ii)angle COD+ angle ODC+ angle OCD = 180° ( sum of property )

angle OCD 180 - 90 - 50

angle OCD 40 °

iii) angle OCD = angle OAB ( alternate interior angle )

∗Therefore , angle OAB= 40 °