Answer:
[tex]20^{\circ}[/tex].
Step-by-step explanation:
Two angles are supplements of one another if their sum is [tex]180^{\circ}[/tex].
Two angles are complements of one another if their sum is [tex]90^{\circ}[/tex].
Let [tex]x^{\circ}[/tex] be the measure of the angle in question.
The supplement of this angle would be [tex](180 - x)^{\circ}[/tex].
The complement of this angle would be [tex](90 - x)^{\circ}[/tex].
According to the question:
[tex](180 - x) + 50 = 3\, (90 - x)[/tex].
Solve this equation for [tex]x[/tex]:
[tex]x = 20[/tex].
Thus, this angle would measure should [tex]20^{\circ}[/tex].
The supplement of this angle would measure [tex](180 - 20)^{\circ} = 160^{\circ}[/tex]. The complement of this angle would measure [tex](90 - 20)^{\circ} = 70^{\circ}[/tex].
Three times the complement of this angle would be [tex]3 \times 70^{\circ} = 210^{\circ}[/tex], which is indeed [tex]50^{\circ}[/tex] greater than the supplement of this angle.
