Question

The diagonal AC and BD of a parallelogram ABCD intersect each other at point O.If angle DAC=32° and angle AOB=70°,then what is the measure of angle DBC?

Answer 1

See the attached fil

Answer 2

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°

•••♪