Question

find the value of x and y in the diagram below. (14x - 10)° 2y° 5x° a. x = 10, y = 25 b. x = 25, y = 10 c. x = 30, y = 50 d. x = 50, y = 130 please select the best answer from the choices provided

Explanation:

Step1: Solve for \(x\)

Since \(5x\) and \(14x - 10\) are vertical angles, they are equal.

$$5x=14x - 10$$

$$10 = 14x-5x$$

$$10 = 9x$$

(This is wrong. Wait, no, correct approach: Since the lines are parallel (by the arrow marks, assume parallel lines and use the property that alternate - interior angles or vertical - like relations. Wait, actually, since \(5x\) and \(14x - 10\) are vertical - angle - like (because of parallel lines and transversal, corresponding angles or vertical - angle equivalence). The correct equation is \(5x+14x - 10=180\) (supplementary angles, same - side interior angles).

$$19x=180 + 10$$

$$19x=190$$

$$x = 10$$

Step2: Solve for \(y\)

Since \(2y\) and \(5x\) are vertical angles (or corresponding angles due to parallel lines), \(2y=5x\). Substitute \(x = 10\) into \(2y=5x\).

$$2y=5\times10$$

$$2y=50$$

$$y = 25$$

Answer:

A. \(x = 10,y = 25\)