Given the diagram, a supplement to

Question

asked Sep 10, 2022 108k views

1 Answer

Milia · Answer 1 · 2022-09-15T01:52:12+0000

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.