Angles 1 and 7 are alternate exterior angles of a transversal cutting two parallel lines. If m(angle1)=4x+10 and m(angle7)=6x+4, what are the measures of angles 1 and 7? Give a property of angles that helped you solve the problem.
What's confusing me about this problem is the fact that angles 1 and 7 are alternate exterior angles. Is this possible with the two lines being parallel?
It’s been ten years still no answer
Bc no one knows
Yes, it is possible for angles 1 and 7 to be alternate exterior angles even when the two lines are parallel.
When two parallel lines are cut by a transversal, such as in this problem, the alternate exterior angles are congruent. This is known as the Alternate Exterior Angles Theorem.
To find the measures of angles 1 and 7, we can set up an equation using the given information.
Since angles 1 and 7 are congruent, we can write the equation as:
4x + 10 = 6x + 4
Now, let's solve for x:
4x - 6x = 4 - 10
-2x = -6
x = -6 / -2
x = 3
Now that we have the value of x, we can substitute it back into either of the original equations to find the measures of angles 1 and 7.
Let's use angle 1:
m(angle1) = 4x + 10
m(angle1) = 4(3) + 10
m(angle1) = 12 + 10
m(angle1) = 22
So, the measure of angle 1 is 22 degrees.
Using the congruence property of alternate exterior angles, we can determine that the measure of angle 7 is also 22 degrees.
Therefore, the measures of angles 1 and 7 are both 22 degrees.
Yes, it is indeed possible for angles 1 and 7 to be alternate exterior angles even with the two lines being parallel. When a transversal intersects two parallel lines, it creates eight angles. Alternate exterior angles are formed when the transversal intersects the two parallel lines on opposite sides of the intersection point.
To find the measures of angles 1 and 7, you need to set up an equation based on the given information. According to the problem, m(angle1) = 4x + 10, and m(angle7) = 6x + 4.
Since angles 1 and 7 are alternate exterior angles, they are congruent. Therefore, their measures will be equal. This is a property of alternate exterior angles.
So, you can set up an equation and solve for x:
4x + 10 = 6x + 4
Subtracting 4x and 4 from both sides, we get:
10 - 4 = 6x - 4x
6 = 2x
Dividing both sides by 2, we get:
x = 3
Now that you have the value of x, you can substitute it back into the expressions for angle 1 and angle 7 to find their measures:
m(angle1) = 4x + 10 = 4(3) + 10 = 22
m(angle7) = 6x + 4 = 6(3) + 4 = 22
Therefore, the measures of angles 1 and 7 are both 22 degrees.
In summary, the property of alternate exterior angles, which states that they are congruent when a transversal intersects two parallel lines, allowed us to set up an equation and find the measures of angles 1 and 7.