Question

angle one and angle 2 form a linear pair. angle 1 is obtuse and angle 2 is 6-3x degrees. find the range of possible values for x

Answer 1

-28 < x < 2

Explanation:

if <1 and <2 form a linear pair, that means they add up to 180 degrees.

<1 + <2 = 180

<1 must be greater than 90 degrees, because that is the definition of an obtuse angle. And we have <2, which is 6-3x.

So <1 + 6 - 3x = 180

Angles can be decimals too so we don't want to say <1's minimum value is 91 degrees. Instead, we will substitute <1 as 90 degrees for our minimum value. And whatever x comes out to be, will be the lower value of our non-inclusive range.

90 + 6 - 3x = 180

-3x = 84

x = -28 (this is our non-inclusive minimum value)

To find our max value, we know that the most <1 can be is 180 degrees because that is the upper limit of an obtuse angle for a linear pair. Again, this will be the non-inclusive upper range value.

180 + 6 - 3x = 180

6 - 3x = 0

6 = 3x

x = 2 (this is our non-inclusive maximum value)

So our final range for x is -28 < x < 2

Hope this helps :)