Question

given m||n, find the value of x. (2x - 29)° (10x + 5)° answer x =

Explanation:

Step1: Use property of parallel lines

When two parallel lines \(m\parallel n\) are cut by a transversal, the corresponding - angles (or alternate - interior angles, or alternate - exterior angles) are equal. Here, assume the two angles \((2x - 29)^{\circ}\) and \((10x+5)^{\circ}\) are either corresponding, alternate - interior or alternate - exterior angles. So we set up the equation \(2x-29 = 10x + 5\).

Step2: Solve the linear equation

First, subtract \(2x\) from both sides of the equation:
\(-29=10x - 2x+5\), which simplifies to \(-29 = 8x+5\).
Then subtract 5 from both sides: \(-29 - 5=8x\), so \(-34 = 8x\).
Finally, divide both sides by 8: \(x=-\frac{34}{8}=-\frac{17}{4}=- 4.25\). But this is incorrect. The correct relationship for these angles is that they are supplementary (since they are same - side interior angles), so \(2x-29+10x + 5=180\).

Step3: Solve the correct equation

Combine like terms: \((2x+10x)+(-29 + 5)=180\), which gives \(12x-24 = 180\).
Add 24 to both sides: \(12x=180 + 24=204\).
Divide both sides by 12: \(x=\frac{204}{12}=17\).

Answer:

\(x = 17\)