Lines p and q are parallel and are intersected by transversal r. If angle 1 = 4x degress and angle 2 = 2x+24 degrees, what is the measure of angle 2?
I do not know the location of angle 1 and 2.
65
To find the measure of angle 2, we need to use the properties of parallel lines intersected by a transversal.
When a transversal intersects two parallel lines, the corresponding angles are congruent.
In this case, angle 1 and angle 2 are corresponding angles because they are on the same side of the transversal, r, and they are formed by the parallel lines, p and q.
So, angle 1 = angle 2.
Given that angle 1 = 4x degrees, we can set up the equation:
4x = 2x + 24
To solve for x, we can subtract 2x from both sides of the equation:
4x - 2x = 2x + 24 - 2x
2x = 24
Now, divide both sides of the equation by 2 to solve for x:
2x/2 = 24/2
x = 12
Now that we have the value of x, we can substitute it back into the equation for angle 2:
angle 2 = 2x + 24
angle 2 = 2(12) + 24
angle 2 = 24 + 24
angle 2 = 48
Therefore, the measure of angle 2 is 48 degrees.