Answer:
The angles measure [tex]65[/tex]° and [tex]115[/tex]°.
Step-by-step explanation:
Supplementary angles are a pair of angles whose measures add up to [tex]180[/tex]°. In this case, we know that one angle is [tex]50[/tex]° bigger than the other one, so if we let the measure of one angle be [tex]x[/tex], then the measure of the other angle will be [tex]x+50[/tex]. Therefore, we can write the following equation to solve for
[tex]x+x+50=180[/tex]
Solving for [tex]x[/tex], we get:
[tex]x+x+50=180[/tex]
[tex]2x+50=180[/tex] (Simplify LHS)
[tex]2x+50-50=180-50[/tex] (Subtract [tex]50[/tex] from both sides of the equation to isolate [tex]x[/tex])
[tex]2x=130[/tex] (Simplify)
[tex]\frac{2x}{2}=\frac{130}{2}[/tex] (Divide both sides of the equation by [tex]2[/tex] to get rid of [tex]x[/tex]'s coefficient)
[tex]x=65[/tex]
Therefore, [tex]x+50=65+50=115[/tex], so our final answer is that the angles measure [tex]65[/tex]° and [tex]115[/tex]°. Hope this helps!
