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A+ Series - Core Mathematics THEORY QUESTIONS Question 1 (SSSCE 2000 Ou 12a) Four angles of a hexagon are 130°, 160°, 112° and 80°. If the remaining angles are equal, find the size of each of them ​

Sagot :

To solve this question, we have to understand the sum of all angles of a polygon, identify the polygon and doing this, we get that the size of each of the angles are: 119º.

Sum of angles:

The sum of angles of a polygon of n sides is given by:

[tex]S_n = 180(n-2)[/tex]

Hexagon:

6 sides, thus [tex]n = 6[/tex], and:

[tex]S_n = 180(6-2) = 180*4 = 720[/tex]

Angles:

Four are 130°, 160°, 112° and 80°, the other two are equal, so both are x. Then:

[tex]130 + 160 + 112 + 80 + x + x = 720[/tex]

[tex]482 + 2x = 720[/tex]

[tex]2x = 238[/tex]

[tex]x = \frac{238}{2}[/tex]

[tex]x = 119[/tex]

Thus, the size of each of them is of 119º.

For more of the angles of a polygon, you can check https://brainly.com/question/19023938

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