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Ber [7]
2 years ago
11

The measure of the smallest angle of a triangle is one-third the measure of the largest

Mathematics
1 answer:
Anton [14]2 years ago
5 0

The biggest angle is 105°, the smallest angle is  35° and the second angle is 40°

A triangle is a polygon that has three sides and three angles. The sum of angles is a triangle is 180 degrees.

<em><u>Types of triangles </u></em>

  • Right angled triangle
  • Isosceles triangle
  • Equilateral triangle
  • Scalene triangle

From the question, the following information was derived:

  • smallest angle = \frac{1}{3}x
  • second angle = x - 65
  • largest angle is represented with x

\frac{1}{3}x + (x - 65 ) + x = 180

Combine similar terms

\frac{1}{3}x + x + x = 180 + 65

Add similar terms together

\frac{7}{3}x = 245

Divide both sides of the equation by 3/7

x = 105

The biggest angle  is 105°

smallest angle =  \frac{1}{3} x 105 = 35°

Second angle = 105 - 65 = 40°

In order to determine the value of each angle, determine the value of the largest angle first and then use the the value to determine the value of the other angles

A similar question was solved here: brainly.com/question/22240750?referrer=searchResults

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Step-by-step explanation:

To calculate ;

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c) the variance of job satisfaction scores for executives and middle managers (to 2 decimals).

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i) For Executive Managers = 1 x 0.05 + 2^2 x 0.09 + 3^2 x 0.03 + 4^2 x 0.42 + 5^2 x 0.41 - 4.05^2 = 1.246 = 1.25

ii) for middle managers ; 1 x 0.04 + 2^2 x 0.10 + 3^2 x 0.12 + 4^2 x 0.46 + 5^2 x 0.28 - 3.84^2 = 1.134 = 1.13

d) the standard deviation of job satisfaction scores for both probability distributions (to 2 decimals). Executives, Middle managers;

For Executives = square root [ 1 x 0.05 + 2^2 x 0.09 + 3^2 x 0.03 + 4^2 x 0.42 + 5^2 x 0.41 - 4.05^2] = 1.12

For Middle Managers ; Square root [1 x 0.04 + 2^2 x 0.10 + 3^2 x 0.12 + 4^2 x 0.46 + 5^2 x 0.28 - 3.84^2 ] = 1.06

e) from the values gotten for the variance of both executive and middle managers, the variance of the former is more than that of the latter as such higher satisfaction with the executive managers.

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