Question

given ( mparallel n ), find the value of ( x ).
answer attempt 2 out of 2
( x=)

Explanation:

Step1: Use the property of consecutive interior angles

When two parallel lines \(m\parallel n\) are cut by a transversal, consecutive interior angles are supplementary. So \((10x - 21)+(10x + 1)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(10x-21 + 10x+1=(10x + 10x)+(-21 + 1)=20x-20\). The equation becomes \(20x-20 = 180\).

Step3: Solve for \(x\)

Add \(20\) to both sides of the equation: \(20x-20+20=180 + 20\), which gives \(20x=200\). Then divide both sides by \(20\): \(x=\frac{200}{20}=10\).

Answer:

\(10\)