Question

1. in the diagram below, transversals t and v intersect parallel lines m and n at point a

what is the value of x?
a 42
48
132
138
at theorem can be used alone to find the measure of ∠a in △abc?
supplementary angle theorem
exterior angle theorem
triangle sum theorem
thagorean theorem

Explanation:

Step1: Use the property of parallel lines and transversals

Since lines \(m\) and \(n\) are parallel, the angle adjacent to \(x\) (let's call it \(y\)) is equal to \(42^{\circ}\) (alternate - interior angles).

Step2: Use the right - angle relationship

We know that \(x + y=90^{\circ}\) (because of the right - angle formed by the intersection of line \(v\) and the horizontal line). Substituting \(y = 42^{\circ}\) into the equation \(x+y = 90^{\circ}\), we get \(x=90^{\circ}-42^{\circ}\).

Answer:

\(x = 48^{\circ}\), so the answer is B.