Question

in $\triangle jkl$, $\overline{jl}$ is extended through point $l$ to point $m$, $\text{m}\angle jkl = (3x + 8)\degree$, $\text{m}\angle ljk = (2x + 20)\degree$, and $\text{m}\angle klm = (7x - 10)\degree$. find $\text{m}\angle ljk$.

answer attempt 1 out of 2
$\text{m}\angle ljk = \square\degree$

Explanation:

Step1: Apply Exterior Angle Theorem

The exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles. In $\triangle JKL$, $\angle KLM$ is an exterior angle, and the two non - adjacent interior angles are $\angle JKL$ and $\angle LJK$. So we have the equation:
$m\angle KLM=m\angle JKL + m\angle LJK$
Substituting the given angle measures:
$(7x - 10)=(3x + 8)+(2x + 20)$

Step2: Simplify and Solve for x

First, simplify the right - hand side of the equation:
$(3x + 8)+(2x + 20)=3x+2x + 8 + 20=5x+28$
So our equation becomes:
$7x-10 = 5x + 28$
Subtract $5x$ from both sides:
$7x-5x-10=5x - 5x+28$
$2x-10 = 28$
Add 10 to both sides:
$2x-10 + 10=28 + 10$
$2x=38$
Divide both sides by 2:
$x=\frac{38}{2}=19$

Step3: Find $m\angle LJK$

We know that $m\angle LJK=(2x + 20)^{\circ}$. Substitute $x = 19$ into this expression:
$m\angle LJK=2(19)+20$
$=38 + 20$
$=58$

Answer:

$58$