Question

Given the diagram, a supplement to

Answer 1

Given:

The figure of a quadrilateral ABCD.

To find:

The supplement of angle ABC.

Solution:

We know that, two angles are called supplementary angles if their sum is 180 degrees.

`\angle ABC+\angle BAC=110^\circ+40^\circ`

`\angle ABC+\angle BAC=150^\circ\\eq 180^\circ`

So,
`\angle BAC` is not a supplement of
`\angle ABC`.

`\angle ABC+\angle ADC=110^\circ+90^\circ`

`\angle ABC+\angle ADC=200^\circ`

So,
`\angle ADC` is not a supplement of
`\angle ABC`.

`\angle ABC+\angle DAB=110^\circ+(40+30)^\circ`

`\angle ABC+\angle DAB=110^\circ+70^\circ`

`\angle ABC+\angle DAB=180^\circ`

So,
`\angle DAB` is a supplement of
`\angle ABC`.

In the same way
`\angle ABC+\angle BDC\\eq 180^\circ`.

So,
`\angle BDC` is not a supplement of
`\angle ABC`.

Therefore, the correct option is C.