Given:
Two parallel lines are cut by a transversal and form a pair of alternate interior angles.
One angle measures (6x + 5)° and the other measure (7x - 4)°
We need to determine the measure of each angle.
Value of x:
Since, the two angles are alternate interior angles, then the two angles are congruent.
Thus, we have;
[tex]6x+5=7x-4[/tex]
[tex]-x+5=-4[/tex]
[tex]-x=-9[/tex]
[tex]x=9[/tex]
Thus, the value of x is 9.
Measure of each angle:
The measure of each angle can be determined by substituting [tex]x=9[/tex] in the measures of each angle.
Thus, we have;
[tex](6x + 5)^{\circ}=(6(9) + 5)^{\circ}=59^{\circ}[/tex]
[tex](7x - 4)^{\circ}=(7(9) - 4)^{\circ}=59^{\circ}[/tex]
Thus, the measure of each angle is 59°
