1. Two lines intersect and determine 4 angles such that the sum of the measures of three of the angles is $322^{\circ}$. What are the measures of each individual angle?
1. 

![](https://cdn.mathpix.com/cropped/2024_05_30_7e3b3cfdf053042fa10ag-05.jpg?height=160&width=503&top_left_y=682&top_left_x=842)

Let the measure of the acute angles be $x^{\circ}$.

The measure of the fourth angle is $360^{\circ}-322^{\circ}=38^{\circ}=x. \quad 2$ points

The measure of the obtuse angle is $180^{\circ}-38^{\circ}=142^{\circ} \quad 1$ point

Therefore, the measures of the required angles are: $38^{\circ}, 142^{\circ}, 38^{\circ}$ and $142^{\circ}$. 1 point

TOTAL 4 POINTS