Question

question
in \\( \triangle qrs, \mathrm{m} \angle q=(2 x+13)^{\circ}, \mathrm{m} \angle r=(2 x+13)^{\circ}, \\) and \\( \mathrm{m} \angle s=(7 x+0)^{\circ} \\). what is the value of \\( x \\)?
answer attempt 1 out of 2
\\( 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.
\((2x+2x + 7x)+(13 + 13+0)=180\), which simplifies to \(11x+26 = 180\).

Step3: Solve for \(x\)

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

Answer:

\(x = 14\)