What is the supplement of 16° ?
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What is the supplement of 16° ?
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Answer:
The definition of a supplement is that the angle and its supplement add to 180° :
Step-by-step explanation:
The supplement of the angle in question is exactly :
3 * the angle - 16° :
\
\
\
\
\ (supplement)
angle ( \ ) 3*angle -16° (angle + supplement = 180°)
angle + supplement = 180°
Subtract supplement from both sides to rearrange for what you don't know:
angle = 180° - supplement
Now use the value for the supplement in the equation:
angle = 180° - (3 * angle - 16°)
Distribute the implied -1 into the parentheses:
angle = 180° - 3*angle + 16°
Combine like terms on the right add 3*angle to both sides to get it to the left of the equation:
angle + 3*angle (1 angle + 3 angles) = 180° + 16°
Combine like terms on the left:
4*angle = 196°
Divide both sides by 4 to isolate what you don't know:
angle = 196°/4
Simplify:
angle = 49°
Now substitute the angle's value in the formula for the supplement angle:
supplement = (3*angle) - 16°
supplement = (3*49°) - 16°
supplement = 147° - 16°
supplement = 131°
Now check to see if both angle and supplement add to 180° to verify your answers:
131° + 49° = 180°
180° = 180° ; verified
Answer:
180°
Step-by-step explanation:
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