Question

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

Answer 1

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.

Step-by-step explanation: exact answer

Answer 2

The other angles will measure 83.9° and 96.1°

Explanation:

If two parallel lines are cut by a transversal and form a pair of alternate exterior angles, then the sum of the two exterior angles will be equal to 180° as shown;

If one angle measures (6x+5) and other measures (7x+4), then;

(6x+5)+(7x+4) = 180° (sum of two exterior angles)

Firstly, lets get the value of x from the equation.

6x+7x+9 = 180°

13x= 180-9

13x = 171

x = 171/13

x = 13.15°

The first angle 6x+5 will measure 6(13.15)+5 = 83.9°

The other angle 7x+4 will mesure 7(13.15)+4 = 96.1°