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.

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

$\angle ABC+\angle BAC=150^\circ\neq 180^\circ$

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 $\angle ABC+\angle BDC\neq 180^\circ$.

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

Therefore, the correct option is C.