## SUBJECT III

Determine the measure of the angle formed by the bisectors of two consecutive angles in a parallelogram.
## SUBJECT III

Consider the parallelogram $A B C D$ and the bisectors of the angles $\angle B A D, \angle A D C$ that intersect at point $E$, as shown in the diagram.

![](https://cdn.mathpix.com/cropped/2024_06_07_9779ca9bc7398744a658g-3.jpg?height=263&width=780&top_left_y=508&top_left_x=615)

$$
\begin{aligned}
& \angle B A D \text { and } \angle A D C \text { are consecutive angles. } \\
& 1 \text { point } \\
& m(\angle B A D)+m(\angle A D C)=180^{\circ} \\
& 2 \text { points } \\
& m(\angle E A D)+m(\angle E D A)=\frac{1}{2} m(\angle B A D)+\frac{1}{2} m(\angle A D C)=\frac{1}{2}[m(\angle B A D)+m(\angle A D C)]=\frac{1}{2} \cdot 180^{\circ}=90^{\circ} \\
& .2 \text { points } \\
& m(\angle A E D)=180^{\circ}-[m(\angle E A D)+m(\angle E D A)]=180^{\circ}-90^{\circ}=90^{\circ} \\
& .2 \text { points. }
\end{aligned}
$$