Question

score: 2/5 penalty: 0.25 off
question
given parallelogram opqr below, ( mangle rso = 100^{circ} ). if ( mangle qsr = (-2x + 10)^{circ} ), solve for ( x ).

Explanation:

Step1: Use linear - pair property

Angles \(\angle QSR\) and \(\angle RSO\) form a linear pair. So, \(m\angle QSR+m\angle RSO = 180^{\circ}\) (linear - pair angles are supplementary).

Step2: Substitute the given values

We know that \(m\angle RSO = 100^{\circ}\) and \(m\angle QSR=(-2x + 10)^{\circ}\). Then \((-2x + 10)+100=180\).

Step3: Simplify the equation

Combine like terms: \(-2x+(10 + 100)=180\), so \(-2x+110 = 180\).
Subtract \(110\) from both sides: \(-2x=180 - 110\), which gives \(-2x=70\).

Step4: Solve for \(x\)

Divide both sides by \(-2\): \(x=\frac{70}{-2}\), so \(x = 45\).

Answer:

\(x = 45\)