Question

What is the name of the angle that is supplementary to angle VST and is its measure?

Answer 1

Please note that two angles are called supplementary when their measures add up to 180 degrees, and two angles are called complementary when their measures add up to 90 degrees.

From the diagram given, the angle that is supplementary to VST is the angle that when add to angle VST would add up to 180 degrees.

The sum of angles on a straight line is 180 degrees, and VST lies on a straight line. Therefore, the angles that would be added to VST is

`\angle VST+\angle VSR=180^0(Angles\text{ on a straight line)}`

From the above, the angle that is supplementary to VST is angle VSR

In other to get the measure of the angle VSR, we would substitute fore the measure of VST given as shown below:

`\begin{gathered} \angle VST+\angle VSR=180^0 \\ \angle VST=76^0(given) \\ So, \\ 76^0+\angle\text{VSR}=180^0 \\ \angle VSR=180^0-76^0 \\ \angle VSR=104^0 \end{gathered}`

Hence, the measure of the angle is 104°