Question

78° (x + 5)° (x + 7)° o x = 45 o x = 46 o x = 49 o x = 51

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, we have the equation \(78+(x + 5)+(x + 7)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(78+x + 5+x + 7=(78 + 5+7)+(x+x)=90 + 2x\). So the equation becomes \(90+2x=180\).

Step3: Solve for \(x\)

Subtract 90 from both sides: \(2x=180 - 90\), so \(2x=90\). Then divide both sides by 2: \(x=\frac{90}{2}=45\).

Answer:

\(x = 45\)