Question

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

Answer 1

Answer:

$20^{\circ}$.

Step-by-step explanation:

Two angles are supplements of one another if their sum is $180^{\circ}$.

Two angles are complements of one another if their sum is $90^{\circ}$.

Let $x^{\circ}$ be the measure of the angle in question.

The supplement of this angle would be $(180 - x)^{\circ}$.

The complement of this angle would be $(90 - x)^{\circ}$.

According to the question:

$(180 - x) + 50 = 3\, (90 - x)$.

Solve this equation for $x$:

$x = 20$.

Thus, this angle would measure should $20^{\circ}$.

The supplement of this angle would measure $(180 - 20)^{\circ} = 160^{\circ}$. The complement of this angle would measure $(90 - 20)^{\circ} = 70^{\circ}$.

Three times the complement of this angle would be $3 \times 70^{\circ} = 210^{\circ}$, which is indeed $50^{\circ}$ greater than the supplement of this angle.