Question

Find the range of possible values of x.
A.
12 < x < 13
B.
3 < x < 12
C.
0 < x < 13
D.
0 < x < 8

Answer 1

Answer: Option C. 0 < x < 13

Solution

We have two triangles IJG and JGH. According with the figure, the two triangles have two congruent sides:

1. Side IJ in triangle IJG is congruent with side GH in triangle JGH.

2. Side GJ in triangle IJG is congruent with side GJ in triangle JGH (Reflexive Property)

The angle between the two congruent sides in triangle JGH (<JGH=35°) is smaller than the anglen between the two congruent sides in triangle IJG (<IJG=59°), then the opposite side to the angle JGH (35°) in triangle JGH must be less than the opposite side to the angle IJG (59°) in triangle IJG:

JH < IG

Replacing JH by x and IG by 13 in the inequality above:

x < 13

And the length of the side JH must be positive:

JH > 0

Replacing JH by x in the inequality above:

x > 0

Then:

x > 0 and x < 13: 0 < x < 13

Answer 2

Answer:

0 < x < 13

Step-by-step explanation:

In the given figure, we have two triangles JIG and JHG.

The sides IJ from the triangle JIG and side GH  from triangle JHG are congruent.

Also, since JG is a common side in both of the triangles so they are also equal.

The angle between these two congruent sides (JG and GH) is 35° which is smaller than the angle between the other congruent sides JG and IJ i.e. 59°.

Therefore, the side JH is also smaller than IG which is 13 so:

x < 13

and JH must be greater than zero, so we can write it as:

0 < x < 13