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the supplement of an angle is 50 less than 3 times its complement, find the measure of the angle

Sagot :

jacob193

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.

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