An angles measure is 6 degrees less than 2 times the measure of its supplement. Find the measure of the angle and its supplement.

Answer 1

Let "x" be the angle. Then the supplement of the angle would be 180 - x because the angle and its supplement must add up to 180°.

2 times the measure of the supplement is "2(180 - x)" and 6 less than that is "2(180 - x) - 6"

So x = 2(180 - x) - 6

Can you solve this for "x" using algebra?

Answer 2

An angle's measure is 6 degrees less than 2 times the measure of its supplement. Find the measure of the angle and its supplement.

An angle: x

is: =

6 degrees less than: ____ - 6° "Something minus 6°"

2 times the measure of its supplement: this is the value that is the "something" in the line above. An angle's supplement is (180 - x)°. Two times that is 2(180 - x)°.

Put it all together...

x = 2(180 - x)° - 6°

Now, solve for x.

x = 360 - 2x - 6

3x = 354

x = 118° ✓

Now, solve for x's supplement.

supplement = (180 -118)° = 62° ✓

Last, check it.

IS x's measure 6° less than 2 times the measure of its supplement?

Well,

2 times the measure of x's supplement is 62° • 2 =124°.

Six degrees less than 124° is 118°. ✓

The angle, x, is 118° and its supplement is 62°.