## Subject I

Angles $\widehat{A O B}$ and $\widehat{A O C}$ are supplementary and non-adjacent. If $m(\widehat{A O B})<m(\widehat{A O C})$ and $m(\widehat{B O C})=40^{\circ}$, calculate the measure of angle $\widehat{D O E}$, where [OD is the bisector of angle $\widehat{A O B}$ and [OE is the opposite ray of ray $[\mathrm{OC}$.
## Subject I

Angles $\overline{A O B}$ and $\overline{A O C}$ are supplementary and non-adjacent. If $m(\widehat{A O B}) < m(\widehat{A O C})$ and $m(\widehat{B O C}) = 40^{\circ}$, calculate the measure of angle $\widehat{D O E}$, where [OD is the bisector of angle $\widehat{A O B}$ and [OE is the opposite ray of ray [OC.

## Scoring:

| Correctly draw angles $\overline{\mathrm{AOB}}$ and $\overline{\mathrm{AOC}}$ non-adjacent | $1 \mathrm{p}$ |
| :--- | :--- |
| $\mathrm{m}(\overline{\mathrm{AOB}}) + \mathrm{m}(\overline{\mathrm{AOC}}) = 180^{\circ}$ | $1 \mathrm{p}$ |
| $\mathrm{m}(\overline{\mathrm{AOB}}) = 70^{\circ} ; \mathrm{m}(\overline{\mathrm{AOC}}) = 110^{\circ}$ | $2 \mathrm{p}$ |
| $\left[\mathrm{OD}\right.$ is the bisector of angle $\overline{A O B} \Rightarrow \mathrm{m}(\overline{\mathrm{AOD}}) = 35^{\circ}$. | $1 \mathrm{p}$ |
| $\left[\mathrm{OE}\right.$ and $\left[\mathrm{OC}\right.$ are opposite rays $\Rightarrow \mathrm{m}(\overline{\mathrm{COE}}) = 180^{\circ}$, thus $\mathrm{m}(\overline{\mathrm{AOE}}) = 70^{\circ}$. | $1 \mathrm{p}$ |
| $\mathrm{m}(\overline{\mathrm{DOE}}) = \mathrm{m}(\overline{\mathrm{DOA}}) + \mathrm{m}(\overline{\mathrm{AOE}}) = 105^{\circ}$ | $1 \mathrm{p}$ |