Hi All,
This question is based on a series of standard Geometry formulas, but you have to stay organized to see how they all 'interact' with one another.
1) Since each triangle consists of 2 radii, each of the triangles is ISOSCELES, meaning that the two base angles are the same. Thus, the three triangles have angles of (70 and 70), (X and X) and (X+1 and X+1).
2) Lines PQ and QS are parallel, so angle PQO (70 degrees) = angle QOS (70 degrees).
3) Quadrilateral QRSO has 4 sides, so its 4 angles total 360 degrees.
The 4 angles that sum to 360 degrees are:
70 + X + (X+X+1) + (X+1) = 360
Combining like terms gives us...
4X + 72 = 360
4X = 288
X = 72
The question asks us for angle ROS. Since the two matching angles are both (X+1), those two angles are 73 and 73, leaving the third angle...
180 - 2(73) = 180 - 146 = 34
Final Answer:
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Rich
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