I need help on this question

which agrees with the first answer listed among the possible options.

Step-by-step explanation:

Notice that if a circle is perfectly inscribed inside the triangle, the triangle must have the symmetries that correspond to an equilateral triangle (all equal sides). Such type of triangles have the three angles equal as well, and since they need to add to , they must measured each

Now, the segment that joins the center of this symmetric triangle (also the center of the circle) with the triangle's vertices, has to bisect each each internal angle in equal parts.

Therefore, angle must measure half of  , that is:  

x is greater than 5

step-by-step explanation:

2x+7 is greater than 17

    -7                           -7

2x is greater than 10

divide by 2 each side

x is greater than 5

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.