Answer:
∠POQ ≈ 26.6°
Explanation:
You want the angle POQ between the lines PO and QO shown in the diagram.
Slope
The slope of a line is equal to the ratio of "rise" to "run". That slope is also the tangent of the angle the line makes with the x-axis.
Line PO has slope 1/1 = 1. The angle it makes with the x-axis is ...
∠PO = arctan(1) = 45°
Line QO has slope 1/3. The angle it makes with the x-axis is ...
∠QO = arctan(1/3) ≈ 18.435°
Angle POQ is the difference between these angles:
∠POQ = 45° -18.435° = 26.565°
∠POQ ≈ 26.6°
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Alternate solution
Another way to find the angle is to use the Law of Cosines.
The side lengths of the triangle POQ can be found using the Pythagorean theorem:
PO = 4√2
QO = 2√(1² +3²) = 2√10
PQ = 2√2
Angle O is given by ...
PQ² = PO² +QO² -2·PO·QO·cos(O) . . . . . . law of cosines
cos(O) = (PO² +QO² -PQ²)/(2·PO·QO)
cos(O) = (32 +40 -8)/(2·4√2·2√10) = 64/(16√20) = 2/√5
O = arccos(2/√5) ≈ 26.565°