Lines x and y are parallel.Use the diagram to determine the measure of the unknown angle.m∠1 = (6x + 8)°m∠1 = 74°1. What is the value of x? _____ Options: 11, 16, 22, 31.2. What is the measure of ∠2? (7x - 2)° + m∠2 = 106°m∠2 = ____° Options: 21, 27, 31, 37.
Accepted Solution
A:
On the bottom line, the 106 and number 1 make a straight line and needs to equal 180 degrees.This means number 1 = 180-106 = 74 degrees.Because x and y are parallel, the top outside angle is the same as number 1.6x +8 = 74Subtract 8 from both sides:6x = 66divide both sides by 6:x = 66 / 6x = 11Now you have x, replace x in the equation for 7x-2 to find that angle:7(11) -2 = 77-2 = 75 degrees. The three inside angles need to equal 180 degrees. Angle 2 = 180 - 74 - 75 = 31 degrees.