Question

1. what is the sum of $d^\circ + e^\circ$? (options: 120°, 160°, 360°, 180°) image of geometric figure with angles and lines

Explanation:

Step1: Identify polygon angle sum

The figure forms a quadrilateral, so the sum of its interior angles is $(4-2)\times180^\circ = 360^\circ$.

Step2: Define known interior angles

The given interior angles are $80^\circ$ and $40^\circ$. The other two interior angles are supplementary to $d^\circ$ and $e^\circ$, so they are $(180-d)^\circ$ and $(180-e)^\circ$.

Step3: Set up angle sum equation

$$80 + 40 + (180-d) + (180-e) = 360$$

Step4: Simplify to solve for $d+e$

$$80+40+180+180 - (d+e) = 360$$
$$480 - (d+e) = 360$$
$$d+e = 480 - 360 = 120$$

Answer:

120°