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secondary 4 | E Maths
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Phil
Phil

secondary 4 chevron_right E Maths chevron_right Singapore

Please How do I find the sum of the stated angles.

Date Posted: 4 years ago
Views: 272
J
J
4 years ago
Sum of interior angles
= (n - 2) x 180°, where n is the number of sides


Sum of all interior angles
= sum of interior angles in quadrilateral + sum of interior angles in the 5 sided polygon

= 180°(4 - 2) + 180°(5 - 2)
= 360° + 540°
= 900°

Or

The whole figure is a 7 sided polygon.

Sum of interior angles
= (n - 2) x 180°, where n is the number of sides

= (7 - 2) x 180°
= 900°


There are 7 vertices. Each vertice has a total angle of 360°.

Sum of all exterior angles
= angle sum of all vertices - angle sum of interior angles

= 360° x 7 - 900°
= 1620°
Phil
Phil
4 years ago
Thanks ^^
J
J
4 years ago
Welcome
Eric Nicholas K
Eric Nicholas K
4 years ago
To add, a prerequisite of this question is that the figures must be fully connected by lines so that a polygon is formed. This method cannot be used if the shape of interest is not a polygon.

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Eric Nicholas K
Eric Nicholas K's answer
5997 answers (Tutor Details)
1st
Something like this would be good.

The question requires us to find the sum of all the external angles of the figure.

We find that there are seven vertices in the figure each having 360 degrees, bringing rise to a total of 2520 degrees in angles.

The sum of interior angles of a square is 360 degrees, while that of pentagon is 540 degrees, both using the formula 180 x (n - 2) for the sum of interior angles of an n-sided polygon.

From there, total sum of external angles
= 2520 - 360 - 540
= 1620 degrees
J
J
4 years ago
The formula can just be applied to the whole heptagon. It works regardless of whether the polygon is concave or convex.