Question

please help me out with this

Answer 1

Answer:

5<x<29

Step-by-step explanation:

One theorem tells us that if a triangle has two congruent sides and one of the included angle is bigger than the other, the triangle with the included angle that is bigger. has a bigger side than the other.

This is the opposite in this case. The triangles share two sides and we know that the triangle with the side length 18 has a bigger angle than the triangle with the side length 15. So this means that

$48 > 2x - 10$

Let find the range of x values.

An angle cannot be negative or zero so this means that

$2x - 10 > 0$

Solve for x.

$2x > 10$

$x > 5$

The angle cannot be bigger than 48 so

$48 > 2x - 10$

Solve for x.

$58 > 2x$

$29 > x$

So x must be greater than 5 but less than 29.