Because [tex]\angle A[/tex] and [tex]\angle B[/tex] are alternate exterior angles, this means they congruent or equal to each other.
Therefore, we can say [tex]5x-15 = 2x+21[/tex] and use this equation to solve for x.
[tex]5x-15 = 2x+21[/tex]
[tex]5x = 2x+36[/tex]
[tex]3x = 36[/tex]
[tex]x = 12[/tex]
So x is equal to 12. After finding this, we can now go back to the equation for [tex]\angle B[/tex] and plugin x to solve it.
[tex]\angle B = 2x +21[/tex]
[tex]\angle B = 2(12) +21[/tex]
[tex]\angle B = 24 +21[/tex]
[tex]\angle B = 45[/tex]
Therefore, [tex]\angle B[/tex] is equal to 45 degrees.
