Question

geometry
parallel lines with transversal practice
find the measures or indicated value:
1.
x = 135° angle pair: ssi
y = 45° angle pair: vertical
z = 45° angle pair: aia
x = 80° angle pair: linear pair
y = 80° angle pair: linear pair
z = angle pair
x = c =
y = d =
z =
a =
b =

Explanation:

Step1: Identify linear - pair relationship for the second set

Since \(x\) and the \(100^{\circ}\) angle are a linear - pair, \(x + 100^{\circ}=180^{\circ}\), so \(x = 80^{\circ}\). \(y\) and \(x\) are vertical angles, so \(y = 80^{\circ}\). \(z\) and the \(100^{\circ}\) angle are alternate - interior angles (AIA), so \(z = 100^{\circ}\).

Step2: Identify angle relationships for the third set

\(x\) and the \(20^{\circ}\) angle are vertical angles, so \(x = 20^{\circ}\). \(y\) and \(x\) are a linear - pair, so \(y=180^{\circ}-20^{\circ}=160^{\circ}\). \(z\) and the \(20^{\circ}\) angle are corresponding angles, so \(z = 20^{\circ}\). \(a\) and \(z\) are vertical angles, so \(a = 20^{\circ}\). \(b\) and \(y\) are vertical angles, so \(b = 160^{\circ}\). \(c\) and \(z\) are a linear - pair, so \(c = 160^{\circ}\). \(d\) and \(a\) are a linear - pair, so \(d = 160^{\circ}\).

Answer:

For the second set: \(z = 100^{\circ}\), Angle Pair: AIA
For the third set:
\(x = 20^{\circ}\)
\(y = 160^{\circ}\)
\(z = 20^{\circ}\)
\(a = 20^{\circ}\)
\(b = 160^{\circ}\)
\(c = 160^{\circ}\)
\(d = 160^{\circ}\)