[tex]\boxed{\angle A=\angle B=45^{\circ}}[/tex]
Here we have two congruent angles ∠A and ∠B. Remember that angles are congruent if they have the same measure, so:
[tex]\angle A=(5x-15)^{\circ} \\ \\ \angle B=(2x+21)^{\circ} \\ \\ \\ \angle A=\angle B \\ \\ \\ So: \\ \\ (5x-15)^{\circ}=(2x+21)^{\circ} \\ \\ \\ Solving \ for \ x: \\ \\ 5x-15=2x+21 \\ \\ 5x-2x=15+21 \\ \\ 3x=36 \\ \\ x=\frac{36}{3} \\ \\ x=12[/tex]
Substituting x in one angle:
[tex]\angle A=(5(12)-15)^{\circ} \\ \\ \angle A=(60-15)^{\circ} \\ \\ \boxed{\angle A=45^{\circ}} \\ \\ \\ Since \ \angle A=\angle B \ then: \\ \\ \boxed{\angle B=45^{\circ}}[/tex]
