Question

this is the only question in this section.
question
in δqrs, m∠q = (2x + 13)°, m∠r = (2x + 13)°, and m∠s = (7x + 0)°. what is the value of x?
answer attempt 1 out of 2
x = blank submit answer

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(m\angle Q + m\angle R + m\angle S = 180^\circ\).

Step2: Substitute angle expressions

Substitute \(m\angle Q=(2x + 13)^\circ\), \(m\angle R=(2x + 13)^\circ\), and \(m\angle S=(7x)^\circ\) into the equation: \((2x + 13)+(2x + 13)+7x = 180\).

Step3: Combine like terms

Combine the \(x\)-terms and constants: \(2x+2x + 7x+13 + 13 = 180\) → \(11x+26 = 180\).

Step4: Solve for \(x\)

Subtract 26 from both sides: \(11x=180 - 26\) → \(11x = 154\). Then divide by 11: \(x=\frac{154}{11}=14\).

Answer:

\(14\)