Question

in \\( \triangle qrs, m\angle q=(2x + 13)^{circ}, m\angle r=(2x + 13)^{circ}, \\) and \\( m\angle s=(7x + 0)^{circ} \\). what is the value of \\( x \\)?

Explanation:

Step1: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(m\angle Q + m\angle R+m\angle S=180^{\circ}\).
Substitute the given angle measures: \((2x + 13)+(2x + 13)+(7x+0)=180\).

Step2: Combine like terms

Combine the \(x\) - terms and the constant terms.
\((2x+2x + 7x)+(13 + 13+0)=180\).
\(11x+26 = 180\).

Step3: Solve for \(x\)

Subtract 26 from both sides of the equation: \(11x+26-26=180 - 26\).
\(11x=154\).
Divide both sides by 11: \(x=\frac{154}{11}\).

Answer:

\(x = 14\)