Question

a designer for a flooring company is laying out a pattern for a hardwood floor. she begins by placing one board across two parallel boards at a diagonal. she needs to find the measures of the angles formed so that the installer will know how to cut the rest of the floorboards. the designers pattern is modeled below. which equations are correct? select all that apply. a = 52 b = 52 c = 52 f = 128 g = 128 h = 128

Explanation:

Step1: Find the value of \(a\)

Since \(a\) and \(128^{\circ}\) are supplementary angles (\(a + 128=180\)), then \(a = 180 - 128=52\).

Step2: Use parallel - line properties

When two parallel lines are cut by a transversal:

• \(b=a\) (alternate interior angles). So \(b = 52\).
• \(c=b\) (vertical angles). So \(c = 52\).
• \(f = 128\) (corresponding angles with the \(128^{\circ}\) angle).
• \(g=f\) (vertical angles). So \(g = 128\).
• \(h

eq128\), \(h=a = 52\) (alternate interior angles with \(a\)).

Answer:

\(a = 52\), \(b = 52\), \(c = 52\), \(f = 128\), \(g = 128\)