2.
2 answers:
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Answer: The answer is only one angle. Explained.
Step-by-step explanation: As given in the question and shown in the attached figure, the lines horizontal lines 'p' and 'q' are cut by the transversal 'r'. We need to determine the least number of angles among the eight angles mentioned in the figure to find the measure of all the angles.
Suppose, the measure of ∠1 is given as x°.
So, ∠2 = 180° - x (linear pair of angles),
∠3 = x (=∠1, vertically opposite angles),
∠4 = 180° - x (=∠2, verticaly opposite angles),
∠1 = ∠5, ∠2 = ∠6, ∠3 = ∠7, ∠4 = ∠8. These are pairs of correspomding angles.
Thus, we need the measure of only one angle to find the measure of all the angles.
Hence explained.
The red area is the one which solves the system. In fact, we want the area which below both the parabola and the line (since the inequality features a sign.
So, the point is below the line but above the parabola (blue area), so it is not a solution.
The point is above both the line and the parabola (white area), so it is not a solution.
The point is below both the line and the parabola (red area), so it is a solution.
So, the point is below the parabola but above the line (green area), so it is not a solution.