Question

Please help, im confused ;w;

Answer 1

`x=7\text{ and } m\angle KLM = 34^\circ`

Explanation:

We are given ethat KM and JN are parallel.

And we want to find the value of x.

Notice that ∠JKM and ∠LKM form a linear pair. Linear pairs total 180°. Therefore:

`m\angle JKM + m\angle LKM = 180`

We know that ∠JKM measures (14x + 8). Substitute:

`(14x+8)+m\angle LKM =180`

Solve for ∠LKM:

`m\angle LKM = 172-14x`

Next, since KM and JN are parallel, by the Corresponding Angles Theorem:

`\angle JNM \cong \angle KML`

Since we know that ∠JNM measure (10x + 2), we can conclude that:

`m\angle KML = 10x+2`

Next, recall that the three interior angles of a triangle must total 180°. Therefore:

`m\angle KLM + m\angle LKM + m\angle KML = 180`

Substitute:

`(5x-1)+(172-14x)+(10x+2)=180`

Solve for x. Rewrite:

`(5x-14x+10x)+(-1+172+2)=180`

Combine like terms:

`(1x)+(173)=180`

Therefore:

`x=7`

To find ∠KLM, substitute in 7 for x and evaluate. So:

`m\angle KLM = 5(7) - 1 =34^\circ`