Problems based on systems of measuring angles will help us to learn converting one measuring systems to other measuring systems. We know, the three different systems are Sexagesimal System, Centesimal System and Circular System. The examples will help us to solve various types of problems involving the three different systems of measuring angles.
Worked-out problems based on systems of measuring angles:
1. Find in sexagesimal, centesimal and circular units an internal angle of a regular Hexagon.
Solution:
We know that the sum of the internal angles of a polygon of n sides = (2n - 4) rt. angles.
Therefore, the sum of the six internal angles of a regular pentagon = (2 × 6 - 4) = 8 rt. angles.
Hence, each internal angle of the Hexagon = 8/6 rt. angles. = 4/3 rt. angles.
Therefore,
each internal angle of the regular Hexagon in sexagesimal system
measures 4/3 × 90°, (Since, 1 rt. angle = 90°) = 120°;
In centesimal system measures
2. Two regular polygons have sides m and n respectively. If the number of degrees in an angle of the first is equal to the number of grades in an angle of the second, show that,
20/n - 18/m = 1.
Solution:
Sum of the internal angles of a regular polygon of m sides = (2m - 4) rt. angles.
Therefore, one angle of a regular polygon of m sides measures (2m - 4)/m rt. angles.
Similarly, one angle of a regular polygon of n sides measures (2n - 4)/n rt. angles.
By question, [(2m - 4)/m] × 90 = [(2n - 4)/n] × 100
or, (1 - 2/m) × 180 = (1 - 2/n) × 200
or, 9 - 18/m = 10 - 20/n
or, 20/n - 18/m = 1. Proved
● Measurement of Angles
From Problems Based on Systems of Measuring Angles to
HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Jun 13, 24 02:51 AM
Jun 13, 24 02:28 AM
Jun 13, 24 12:11 AM
Jun 12, 24 01:11 PM
Jun 11, 24 07:15 PM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.