Basic question about angles

Question

• Why is the answer a)? Why can't it be d)?
• Why are the choices listed in this format, i.e., $(x \pm \theta^{\circ})$, and why is angle C $(x+30^{\circ})$ and not just $30^{\circ}$?

Thanks.

Answer 1

The $x$ is there just to make the question slightly abstract. Perhaps the question author thought this bit of abstraction would better test your comfort with triangles and variables.

You ask why the answer cannot be d). Let's check by assigning $x$ a particular value, like $0^\circ$. In this case, $C$ has angle $30^\circ$, so we know that $A$ has angle $60^\circ$. Option d) would say that $A$ has $-60^\circ$. Why is that negative there? It shouldn't be, as we're not using oriented angles.

Answer 2

You know that the internal angles of a triangle add up to $180$ and you know $B$ is a right angle so we have $180 = A + B + C = A + 90 + C$ and so $A + C = 90$.

We are given that $x+30 = C$ and so $A + x + 30 = 90$ and so $A = 60 - x$.

Answer 3

• $A$ and $C$ wouldn't be complementary angles in that case.

• They give it as $x+30^\circ$ because they want you to consider it symbolically (i.e. it would be equally applicable to an angle of $35^\circ$, or $40^\circ$, etc.)