Question

look at the diagram. which equation can be used to solve for x? 6x + 42 = 180 3x + 45 = 180 6x + 48 = 180 3x + 51 = 180 solve for x. x =

Explanation:

Step1: Note angle - sum property

The angles around point $G$ form a straight - line, so the sum of the angles $48^{\circ}$, $90^{\circ}$ and $(3x + 3)^{\circ}$ is $180^{\circ}$.

Step2: Set up the equation

$48+90+(3x + 3)=180$.

Step3: Simplify the left - hand side

First, add the constant terms: $48 + 90+3=141$. The equation becomes $3x+141 = 180$. This is equivalent to $3x=180 - 141$, or $3x + 39=0$. Another way is to consider the non - right - angle parts. The non - right angles are $48^{\circ}$ and $(3x + 3)^{\circ}$, and their sum with the right - angle ($90^{\circ}$) is $180^{\circ}$. So, $48+(3x + 3)=90$. Simplifying the left - hand side gives $3x+51 = 180$.

Step4: Solve for $x$

Subtract 51 from both sides of the equation $3x + 51=180$: $3x=180 - 51$. So, $3x = 129$. Then divide both sides by 3: $x=\frac{129}{3}=43$.

Answer:

The equation is $3x + 51 = 180$, $x = 43$