Points U and V mark a circle of a 150-degree arc, and point W divides another arc into parts UW and VW

| January 13, 2021 | education

Points U and V mark a circle of a 150-degree arc, and point W divides another arc into parts UW and VW, which are 3: 4 related. Find the corners of the triangle.

The three arcs UV, VW and WU together make up a full circle, that is, 360 °. Let UW be 3x, then VW 4x. Let’s make the equation:
150 + 3x + 4x = 360.
7x = 360 – 150.
7x = 210.
x = 210: 7.
x = 30 °.
Hence, the arc UW = 3x = 3 * 30 = 90 °, and the arc VW = 4x = 4 * 30 = 120 °.
The angle V of the triangle UVW rests on the arc UW, so the angle V = UW / 2 = 90: 2 = 45 °.
The angle U rests on the VW arc, so the angle U = VW / 2 = 120: 2 = 60 °.
The angle W rests on the arc UV, so the angle W = UV / 2 = 150: 2 = 75 °.
Check (the sum of the angles of the triangle is 180 °):
45 + 60 + 75 = 120 + 60 = 180 ° (correct).
Answer: 45 °, 60 °, 75 °.



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