Question

l is in the interior of ∠ijk. if m∠ijl = (76 - 6x)°, m∠ljk = (90 - 8x)°, and m∠ijk = (28 + 9x)°, find the value of x.

Explanation:

Step1: Apply angle - addition postulate

$m\angle IJL+m\angle LJK = m\angle IJK$
$(76 - 6x)+(90 - 8x)=28 + 9x$

Step2: Combine like - terms on left side

$76+90-6x - 8x=28 + 9x$
$166-14x=28 + 9x$

Step3: Add $14x$ to both sides

$166=28 + 9x+14x$
$166=28 + 23x$

Step4: Subtract 28 from both sides

$166 - 28=23x$
$138 = 23x$

Step5: Divide both sides by 23

$x=\frac{138}{23}$
$x = 6$

Answer:

$x = 6$