Question

Alright I've tried everything to try and do this but I'm still struggling. Help. Find the value of x (32 points clear explanation, please)

Answer 1

C. 37.5

Explanation:

From inspection of the given triangle, we can see that the straight line that divides the triangle into two smaller triangles is an angle bisector since it divides the angle into two congruent angles.

Angle Bisector Theorem

An angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.

`\implies x:15=40:16`

Solve for x:

`\implies (x)/(15)=(40)/(16)`

`\implies (x)/(15)=2.5`

`\implies x=2.5* 15`

`\implies x=37.5`