Final answer:
To find the measure of angle 2, set up an equation using the given information and solve for x. Then substitute the value of x into the equation for angle 2 to find its measure.
Step-by-step explanation:
To find the measure of angle 2, we can set up an equation using the given information. We have m∠2 = 6x and m∠27 = 4x + 20. Since m∠2 and m∠27 are measures of angles, they must add up to 180 degrees.
So, 6x + (4x + 20) = 180. Simplifying the equation gives us 10x + 20 = 180. Next, we can subtract 20 from both sides: 10x = 160. Finally, divide both sides by 10 to solve for x: x = 16.
Now that we have the value of x, we can find the measure of angle 2. Substituting x = 16 into the equation m∠2 = 6x gives us m∠2 = 6(16) = 96 degrees.