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. a = 52 b. b = 52 c. c = 52 d. f = 128

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. The angle opposite the \(128^{\circ}\) angle is also \(128^{\circ}\). Adjacent angles to the \(128^{\circ}\) angle are supplementary (sum to \(180^{\circ}\)). Let's find the adjacent angles. If we call an adjacent angle \(x\), then \(x + 128^{\circ}=180^{\circ}\), so \(x = 180^{\circ}-128^{\circ}=52^{\circ}\).

Step2: Identify angle - equal relationships

The angles \(a\), \(b\), and \(c\) are all adjacent to the \(128^{\circ}\) angles and are equal to \(52^{\circ}\) because of the properties of angles formed by two parallel lines and a transversal (corresponding, alternate - interior, etc. and vertical - angle relationships). The angle \(f\) is a vertical angle to the \(128^{\circ}\) angle, so \(f = 128^{\circ}\).

Answer:

A. \(a = 52\)
B. \(b = 52\)
C. \(c = 52\)
D. \(f=128\)