Question

the diagram shows a triangle. what is the value of x? x = □°

Explanation:

Step1: Recall angle - sum property

The sum of interior angles of a triangle is 180°. So, $(2x - 47)+(2x - 42)+(2x - 49)=180$.

Step2: Combine like - terms

Combine the x - terms and the constant terms: $(2x+2x + 2x)+(-47-42 - 49)=180$, which simplifies to $6x-138 = 180$.

Step3: Isolate the variable term

Add 138 to both sides of the equation: $6x-138 + 138=180 + 138$, resulting in $6x=318$.

Step4: Solve for x

Divide both sides by 6: $\frac{6x}{6}=\frac{318}{6}$, so $x = 53$.

Answer:

$53$