Question

find the value of each variable. 16. (3x + 6)° 54° (3x + 6)+54 = 180 3x + 60 = 180 -60 -60 3x = 120 3x/3 = 120/3 x = 40

Explanation:

Step1: Set up equation based on linear - pair

Since the two angles $(3x + 6)^{\circ}$ and $54^{\circ}$ form a linear - pair, their sum is $180^{\circ}$. So, $(3x + 6)+54=180$.

Step2: Simplify the left - hand side

Combine like terms: $3x+(6 + 54)=180$, which gives $3x+60 = 180$.

Step3: Isolate the term with $x$

Subtract 60 from both sides of the equation: $3x+60-60=180 - 60$, resulting in $3x=120$.

Step4: Solve for $x$

Divide both sides of the equation by 3: $\frac{3x}{3}=\frac{120}{3}$, so $x = 40$.

Answer:

$x = 40$