Question

The diagonal ac and bd of a parallelogram abcd intersect each other at o if anglecad=32 and angle aob=70 find angledbc

Answer 1

Answer:

<DBC = 38°

Step-by-step explanation:

Given:

ABCD is a parallelogram .

AC,BD diagonals intersecting at "O".

<DAC = 32°, <AOB = 70°

Proof:

i) AB//DC , AC is a transversal.

<DAC = <BCA = 32°

/* Alternate angles */

ii) In ∆BCO , CO extended to A.

Sum of interior opposite angles = Exterior angle at O

=> <BCA + <OBC = <AOB

=> <BCA + <DBC = <AOB

=> 32° + <DBC = 70°

=> <DBC = 70°-32°

=> <DBC = 38°

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