Question

1. $mangle efg = 130^{circ}, mangle lfg = x + 71$, and $mangle efl = x + 71$. find $x$.

Explanation:

Step1: Use angle - addition postulate

Since $\angle EFG=\angle EFL+\angle LFG$, we can substitute the given angle - measures. So, $130=(x + 71)+(x + 71)$.

Step2: Simplify the right - hand side

Combine like terms: $130 = 2x+142$.

Step3: Solve for $x$

Subtract 142 from both sides: $130−142=2x$, which gives $- 12 = 2x$. Then divide both sides by 2: $x=\frac{-12}{2}=-6$.

Answer:

$x = - 6$