Question

Two parallel lines are cut by a transversal and form a pair of alternate exterior angles. One angle measures (6x + 5)° and the other measures (7x – 4)°. Explain how to determine what those angles actually measure?

Answer 1

Well, alternate exterior angles are congruent. They will have the same measure. They are equal to each other.

6x+5= 7x-4

Add 4 to both sides.

6x+9= 7x

Subtract 6x on both sides.

9=x

Now, plug in 9 for the measures of the angles.

6(9)+5
54+5= 59

7(9)-4
63-4= 59

The angles equal 59 degrees.

I hope this helps!
~kaikers

Answer 2

Sample Response: Since the lines are parallel, the alternate exterior angles are congruent. Therefore you can set the expressions equal to each other and solve for x. Then you can substitute the value of x back into either expression to find the angle measure.