Respuesta :
Answer:
The angle measures 72°
Step-by-step explanation:
Convert the given statements into equations.
*Know that complementary angles add up to 90° and supplementary angles add up to 180°
"The supplement of an angle is six times as large as the complement of the angle" becomes....
180° - a = 6(90° - a)
**180° - a is the supplement. If angle + supplement = 180°, then
180° - angle = supplement
**90° - a is the complement. If angle + complement = 90°, then
180° - angle = complement
Now solve the equation 180° - a = 6(90° - a)
180° - a = 540° - 6a (distribute the 6 on the right side)
6a - a = 540° - 180° (bring variables to one side, and constants
to the other)
5a = 360° (simply both sides)
a = 72° (Solve for a by dividing both sides by 5)
***This makes the complement 18° (72 + 18 = 90)
and the supplement 108° (72 + 108 = 180). We can see that 108 = 6(18) so we have the right answer!
