For any triangle, think about how an exterior angle compares to the two interior angles that are not adjacent to it. How can you express $m\angle ACD$ in terms of $m\angle A$ and $m\angle B$?

Let $m\angle A = x$. Use the fact that $m\angle B = 48^\circ$ and $m\angle ACD = 117^\circ$ to write an equation involving $x$, then solve for $x$.

After you find $m\angle A$, you can confirm your answer by finding the interior angle at $C$ (it forms a straight line with $\angle ACD$) and checking that all three interior angles of the triangle add to $180^\circ$.

Using the exterior angle relationship $m\angle A + 48 = 117$, type 117 - 48 into Desmos and use the result as the measure of $\angle A$ (in degrees).

In a triangle, an exterior angle equals the sum of the two remote interior angles (the two interior angles that are not adjacent to the exterior angle).

Here, $\angle ACD$ is the exterior angle at $C$, and the remote interior angles are $\angle A$ and $\angle B$.

So we can write:

We are given:

• $m\angle B = 48^\circ$
• $m\angle ACD = 117^\circ$

Substitute these into the equation from Step 1:

Isolate $m\angle A$ by subtracting $48^\circ$ from both sides:

So the measure of angle $A$ is $69^\circ$, which corresponds to choice B).