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  2. Clock angle problem - Wikipedia

    en.wikipedia.org/wiki/Clock_angle_problem

    A method to solve such problems is to consider the rate of change of the angle in degrees per minute. The hour hand of a normal 12-hour analogue clock turns 360° in 12 hours (720 minutes) or 0.5° per minute. The minute hand rotates through 360° in 60 minutes or 6° per minute. [1]

  3. Internal and external angles - Wikipedia

    en.wikipedia.org/wiki/Internal_and_external_angles

    The interior angle concept can be extended in a consistent way to crossed polygons such as star polygons by using the concept of directed angles.In general, the interior angle sum in degrees of any closed polygon, including crossed (self-intersecting) ones, is then given by 180(n–2k)°, where n is the number of vertices, and the strictly positive integer k is the number of total (360 ...

  4. Angle trisection - Wikipedia

    en.wikipedia.org/wiki/Angle_trisection

    For example, ⁠ 3 π / 7 ⁠ is such an angle: five angles of measure ⁠ 3 π / 7 ⁠ combine to make an angle of measure ⁠ 15 π / 7 ⁠, which is a full circle plus the desired ⁠ π / 7 ⁠. For a positive integer N , an angle of measure ⁠ 2 π / N ⁠ is trisectible if and only if 3 does not divide N .

  5. Angle - Wikipedia

    en.wikipedia.org/wiki/Angle

    The supplement of an interior angle is called an exterior angle; that is, an interior angle and an exterior angle form a linear pair of angles. There are two exterior angles at each vertex of the polygon, each determined by extending one of the two sides of the polygon that meet at the vertex; these two angles are vertical and hence are equal.

  6. Langley's Adventitious Angles - Wikipedia

    en.wikipedia.org/wiki/Langley's_Adventitious_Angles

    The article contains a history of the problem and a picture featuring the regular triacontagon and its diagonals. In 2015, an anonymous Japanese woman using the pen name "aerile re" published the first known method (the method of 3 circumcenters) to construct a proof in elementary geometry for a special class of adventitious quadrangles problem.

  7. Solid angle - Wikipedia

    en.wikipedia.org/wiki/Solid_angle

    The solid angle of a sphere measured from any point in its interior is 4 π sr. The solid angle subtended at the center of a cube by one of its faces is one-sixth of that, or 2 π /3 sr. The solid angle subtended at the corner of a cube (an octant) or spanned by a spherical octant is π /2 sr, one-eight of the solid angle of a sphere. [1]