In a triangle, we know that the sum of the angles must equal to 180°.
And we also know that two supplementary angles must equal to 180°.
That being said, we are given the value of ∠C as 75°.
In order to solve for ∠B, we must first calculate it. ∠B is part of a supplementary angle, which we know the other angle is equal to 122°. In order to find ∠B, we must subtract 122° from 180°:
[tex]180-122=58[/tex]
So now we know that ∠B is equal to 58°.
So we know the values of two angles of the triangle. In order to solve for the third angle, we must subtract the two known angles values from 180°:
[tex]180-75-58=47[/tex]
And now we know that ∠A is equal to 47°.
