Question

Please help me out with this

Answer 1

5<x<29

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.