Question

1. solve for x. then find angle rsq.

find the measure of \\( \angle r s q \\).

\\( m \angle r s q = \square ^ { \circ } \\)
x:
angle rsq:

Explanation:

Step1: Use the property of corresponding angles

Since \(NO\parallel PQ\), the corresponding angles are equal. So, \(5x + 86=10x + 46\).

Step2: Solve the equation for \(x\)

Subtract \(5x\) from both sides: \(86 = 5x+46\).
Subtract \(46\) from both sides: \(5x=86 - 46\), so \(5x = 40\).
Divide both sides by \(5\): \(x=\frac{40}{5}=8\).

Step3: Find the measure of \(\angle RSQ\)

Substitute \(x = 8\) into \(10x + 46\).
\(10\times8+46=80 + 46=126\).

Answer:

\(x = 8\); Angle \(RSQ=126^{\circ}\)