Question

on your own: exterior angles of a trian
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$x = \square$
the triangle has an interior angle of $(3x + 2)^\circ$, an interior angle of $40^\circ$, and an exterior angle of $132^\circ$ at the vertex adjacent to the third interior angle.

Explanation:

Step1: Find interior adjacent angle

The interior angle adjacent to the 132° exterior angle is $180^\circ - 132^\circ = 48^\circ$.

Step2: Set up triangle angle sum

Sum of triangle angles is $180^\circ$.
$$48^\circ + 40^\circ + (3x + 2)^\circ = 180^\circ$$

Step3: Simplify and solve for x

Combine constants first: $48 + 40 + 2 + 3x = 180$
$$90 + 3x = 180$$
$$3x = 180 - 90$$
$$3x = 90$$
$$x = \frac{90}{3} = 30$$

Answer:

$x = 30$