Question

question 2 (3 points)
if m∠def=(6x + 2): m∠deg=(4x + 1): and m∠gef = 19, find the value of x and the measure of each angle.
x=
m∠deg=
m∠def=

Explanation:

Step1: Use angle - addition postulate

Since $\angle DEF=\angle DEG+\angle GEF$, we have the equation $(6x + 2)=(4x + 1)+19$.

Step2: Simplify the right - hand side

$(4x + 1)+19=4x+20$, so the equation becomes $6x + 2=4x+20$.

Step3: Isolate the variable terms

Subtract $4x$ from both sides: $6x-4x + 2=4x-4x+20$, which simplifies to $2x+2 = 20$.

Step4: Isolate the variable

Subtract 2 from both sides: $2x+2 - 2=20 - 2$, getting $2x=18$. Then divide both sides by 2: $\frac{2x}{2}=\frac{18}{2}$, so $x = 9$.

Step5: Find the measure of $\angle DEG$

Substitute $x = 9$ into the expression for $\angle DEG$: $m\angle DEG=4x + 1=4\times9+1=36 + 1=37$.

Step6: Find the measure of $\angle DEF$

Substitute $x = 9$ into the expression for $\angle DEF$: $m\angle DEF=6x + 2=6\times9+2=54+2=56$.

Answer:

$x = 9$
$m\angle DEG=37$
$m\angle DEF=56$