Answer:
B. [tex]70^{\circ}[/tex].
Step-by-step explanation:
Let x be the required angle and y be its complement and z be its supplement.
We have been given that the sum the measures of a complement and a supplement of an angle is 200.
[tex]x+y+z=200^{\circ}...(1)[/tex]
We know that complementary angles add up-to 90 degrees, so we can set an equation as:
[tex]x+y=90^{\circ}...(2)[/tex]
We know that supplementary angles add up-to 180 degrees, so we can set an equation as:
[tex]x+z=180^{\circ}....(3)[/tex]
We will use substitution method to solve our given equation. From equation (2) and (3) we will get,
[tex]y=90^{\circ}-x[/tex]
[tex]z=180^{\circ}-x[/tex]
Substituting these values in equation (1) we will get,
[tex]x+90^{\circ}-x+180^{\circ}-x=200^{\circ}[/tex]
Combine like terms:
[tex]-x+270^{\circ}=200^{\circ}[/tex]
[tex]-x+270^{\circ}-270^{\circ}=200^{\circ}-270^{\circ}[/tex]
[tex]-x=-70^{\circ}[/tex]
[tex]x=70^{\circ}[/tex]
Therefore, the measure of the required angle is 70 degrees and option B is the correct choice.
