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The angle between the minute hand and the hour hand of a clock when the time is 7 : 20 a.m. is
The angle between the minute hand and the hour hand of a clock at 7:20 a.m. is 100 degrees.
To find the angle between the minute hand and the hour hand of a clock at 7:20 a.m., we can use the following formula:
Angle = |(30 × hour) – (11/2 × minutes)|
Where:
- hour is the hour on the clock
- minutes is the minutes on the clock
For 7:20 a.m.:
Substitute the values into the formula:
Angle = |(30 × 7) – (11/2 × 20)| Angle = |(210) – (110)| Angle = |100| Angle = 100 degrees
So, the angle between the minute hand and the hour hand of a clock at 7:20 a.m. is 100 degrees.
Angles and Degrees in Mathematics
In mathematics, angles are geometric figures formed by two rays or line segments that share a common endpoint, called the vertex. Angles are typically measured in degrees or radians, with degrees being the more common unit in everyday usage.
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Here are some key concepts related to angles and degrees:
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Degree: The degree is a unit of measurement for angles. A full rotation around a point is divided into 360 degrees. This convention is derived from ancient Babylonian mathematics.
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Types of Angles:
- Acute Angle: An angle measuring less than 90 degrees.
- Right Angle: An angle measuring exactly 90 degrees. It forms a perfect ‘L’ shape.
- Obtuse Angle: An angle measuring greater than 90 degrees but less than 180 degrees.
- Straight Angle: An angle measuring exactly 180 degrees. It forms a straight line.
- Reflex Angle: An angle measuring greater than 180 degrees but less than 360 degrees.
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Complementary Angles: Two angles are complementary if their sum equals 90 degrees.
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Supplementary Angles: Two angles are supplementary if their sum equals 180 degrees.
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Adjacent Angles: Adjacent angles share a common vertex and a common side, but do not overlap.
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Vertical Angles: Vertical angles are formed by the intersection of two lines and are opposite each other. They are always congruent (i.e., have the same measure).
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Measuring Angles: Angles are typically measured using a protractor, a tool specifically designed for this purpose. The angle is measured by aligning the center of the protractor with the vertex of the angle and reading the degree measure where the other ray intersects the protractor scale.
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Degrees in a Circle: A full circle is 360 degrees. This convention makes calculations and measurements of angles in circles straightforward.
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Converting Between Degrees and Radians: Radians are another unit of angle measurement commonly used in advanced mathematics. One full circle equals 2π radians. To convert from degrees to radians, multiply by 180π, and to convert from radians to degrees, multiply by 180π.
Understanding angles and degrees is fundamental in geometry, trigonometry, and many other branches of mathematics and sciences where spatial relationships are important.
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