Answer:
[tex]\angle A=30^\circ\\\angle B=60^\circ\\\angle C=105^\circ[/tex]
Step-by-step explanation:
Since [tex]\angle C[/tex] and [tex]75^\circ[/tex] are supplementary angles, they add up to [tex]180^\circ[/tex]. So, [tex]\angle C=180^\circ-75^\circ=105^\circ[/tex].
Also, since [tex]\angle A[/tex] and [tex]30^\circ[/tex] are vertical angles, they have the same angle measure as the angles are congruent to each other. So, [tex]\angle A=30^\circ[/tex].
We can easily figure out [tex]\angle B[/tex] because we have the measurement of [tex]\angle A[/tex] and a given right angle, which measures [tex]90^\circ[/tex]. Thus, by the Triangle Angle-Sum Theorem, all the interior angles of that triangle must add up to [tex]180^\circ[/tex], so [tex]\angle A+\angle B+90^\circ=180^\circ[/tex] must hold true. Hence, [tex]30^\circ+\angle B+90^\circ=180^\circ\rightarrow \angle B=60^\circ[/tex].
