Angles 1 and 7 are alternate exterior angles of a transversal cutting two parallel lines. If m(�Ú1)=4x+10 and m(�Ú7)=6x+4, what are the measures of angles 1 and 7? Give a property of angles that helped you solve the problem.
What's throwing me off a bit on this problem is the fact that angles 1 and 7 are alternate exterior angles. Is this possible with the two lines being parallel?
To find the measures of angles 1 and 7, we can make use of the property of alternate exterior angles. In the case of a transversal intersecting two parallel lines, alternate exterior angles are congruent. Hence, we can set up an equation by equating the measures of angles 1 and 7.
Since m(�Ú1) is given as 4x + 10 and m(�Ú7) is given as 6x + 4, we can set up the equation:
4x + 10 = 6x + 4
Now, let's solve this equation to find the value of x, which will help us determine the measures of angles 1 and 7.
Subtracting 4x from both sides:
10 = 2x + 4
Subtracting 4 from both sides:
6 = 2x
Dividing by 2:
3 = x
Now that we know the value of x, we can substitute it back into the expressions for m(�Ú1) and m(�Ú7) to find their respective measures.
For angle 1:
m(�Ú1) = 4x + 10 = 4(3) + 10 = 22
For angle 7:
m(�Ú7) = 6x + 4 = 6(3) + 4 = 22
So, angle 1 and angle 7 both measure 22 degrees.
The property of alternate exterior angles helped us solve this problem by allowing us to equate the measures of angles 1 and 7, since they are congruent as alternate exterior angles.