Question

ab and cd intersect at point f. if m∠afc = (2x − 4)° and m∠afd = (34y − 12)°, what are the values of x and y such that ab is perpendicular to cd? select all that apply. a) x = 3 b) x = 47 c) x = 90 d) y = 3 e) y = 47 f) y = 90

Explanation:

Step1: Determine angle measure for perpendicular lines

If \(\overleftrightarrow{AB}\) is perpendicular to \(\overleftrightarrow{CD}\), then the intersecting angles are \(90^\circ\). So \(m\angle AFC = 90^\circ\) and \(m\angle AFD=90^\circ\).

Step2: Solve for \(x\)

Given \(m\angle AFC=(2x - 4)^\circ\) and \(m\angle AFC = 90^\circ\) (since perpendicular), set up the equation:
\(2x-4 = 90\)
Add 4 to both sides: \(2x=90 + 4=94\)
Divide by 2: \(x=\frac{94}{2}=47\)

Step3: Solve for \(y\)

Given \(m\angle AFD=(34y - 12)^\circ\) and \(m\angle AFD = 90^\circ\) (since perpendicular), set up the equation:
\(34y-12=90\)
Add 12 to both sides: \(34y=90 + 12 = 102\)
Divide by 34: \(y=\frac{102}{34}=3\)

Answer:

B) \(x = 47\)
D) \(y = 3\)