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ACT style question - Angles - Geometry











































Can you please help me with this ACT question
I can get it down to the correct 2 but cant figure out the difference between H and K
both seem to work
thanks
Thomas

Comments for ACT style question - Angles - Geometry

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Mar 25, 2012
Angles - Geometry
by: Staff


Question:


Can you please help me with this ACT question
I can get it down to the correct 2 but cant figure out the difference between H and K
both seem to work
thanks
Thomas


Answer:

60. In the figure below, the measure of ∠ABC is (x + 40)°and the measure of ∠BCD is (2x + 20) °. What are all the values of x such that the measures of ∠ABC and ∠BCD must be between 0 and 180°and AB is not parallel to CD?


“If” AB and CD were parallel, then ∠A and ∠BCD would be equal.

Since this is not the case, there are only two possibilities:

∠A < ∠BCD or ∠A > ∠BCD.


180 - (x + 40)< (2x + 20)

or

180 - (x + 40)> (2x + 20)

In either case, you can solve for x.

------------------------------------------

If ∠A < ∠BCD


180 - (x + 40)< (2x + 20)

180 - x – 40 < 2x + 20

180 - x – 40 + x < 2x + 20 + x

180 – 40 - x + x < 2x + x + 20

(180 – 40) + (- x + x) < (2x + x) + 20

140 + 0 – 40 < 3x + 20

140 < 3x + 20

140 - 20 < 3x + 20 - 20

120 < 3x + 0

120 < 3x

120/3 < 3x/3

120/3 < x*(3/3)

120/3 < x*(1)

120/3 < x

40 < x


------------------------------------------

If ∠A > ∠BCD:


180 - (x + 40) > (2x + 20)

180 - x – 40 > 2x + 20

180 - x – 40 + x > 2x + 20 + x

180 – 40 - x + x > 2x + x + 20

(180 – 40) + (- x + x) > (2x + x) + 20

140 + 0 – 40 > 3x + 20

140 > 3x + 20

140 - 20 > 3x + 20 - 20

120 > 3x + 0

120 > 3x

120/3 > 3x/3

120/3 > x*(3/3)

120/3 > x*(1)

120/3 > x

40 > x

x < 40




x ≠ 40


>>> the final answer is: x ≠ 40°(choice F)



Thanks for writing.

Staff
www.solving-math-problems.com



Sep 30, 2016
much easier NEW
by: Anonymous

Just find out when they sum to 180. That is the x you exclude.

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