Question

2.4 | parallel & perpendicular | hw #4
in the diagram, \\( \overleftrightarrow { r s } \perp \overleftrightarrow { s t } \\). find the value of x.
\\( x = \\)

Explanation:

Step1: Use the property of perpendicular lines

Since \(\overleftrightarrow{RS}\perp\overleftrightarrow{ST}\), the sum of the angles \((2x + 10)^{\circ}\) and \((5x-4)^{\circ}\) is \(90^{\circ}\). So, we can write the equation \(2x + 10+5x - 4=90\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((2x+5x)+(10 - 4)=90\), which gives \(7x+6 = 90\).

Step3: Solve for \(x\)

Subtract \(6\) from both sides of the equation: \(7x+6-6=90 - 6\), so \(7x=84\).
Divide both sides by \(7\): \(x=\frac{84}{7}\).

Answer:

\(12\)