in the given figure angle A+ angle B+ angle C +angle D+ angle E is equal to
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Answers
Answer:
Consider the given figure.
FGHIJ form a regular pentagon. Now the sum of all angles of a pentagon is
=(n−2)×180
n=5
=(5−2)×180
0
=3×180
0
=540
0
.
Since it is a regular pentagon, hence
∠F=∠G=∠H=∠I=∠J=
5
540
0
=108
0
.
Now
∠AGF=180
0
−∠FGH=180
0
−108=72
0
(linear pair).
Similarly
∠AFG=180
0
−∠GFJ=180
0
−108=72
0
.
Hence ∠A=180
0
−(72
0
+72
0
))=180
0
−144
0
=36
0
...(angles sum property of triangle applied to triangle AFG).
Similarly
∠B=36
0
, ∠C=36
0
, ∠D=36
0
and ∠E=36
0
.
Therefore
∠A+∠B+∠C+∠D+∠E=5×36
0
=180
0
=π.
solution
pls don't think that I had taken this answer from Google.
in my class 10th I'm having this same question so I know .
This diagram I had drawn in white board app and taken screenshot, and I puted here....☺☺
Concept:
When two angles are added together, complementary and supplementary angles are defined. Two angles are said to be supplementary angles because they combine to generate a linear angle when their sum is 180 degrees. When two angles add up to 90 degrees, however, they are said to be complimentary angles and together they make a right angle.
Given:
A 5 point star
Find:
in the given figure angle A+ angle B+ angle C +angle D+ angle E is equal to
Solution:
Consider the given figure.
FGHIJ form a regular pentagon. Now the sum of all angles of a pentagon is
=(n−2)×180
Since,n=5
=(5−2)×180
=3×180
=540
Since it is a regular pentagon, hence
∠F=∠G=∠H=∠I=∠J=
Each angle in a regular polygon has the same size. Each inner angle is 108 degrees.
Its supplementary angle is 180 - 108 = 72.
As a result of the star's isosceles triangles, the other angle at the base measures 72 degrees.
An angle's vertex measurement is 180 72 72 = 36.
Every angle at a star's vertices measures 36 degrees.
As a result, the star's five vertices' total angle = 5x 36 = 180.
The solution is therefore 180°.
#SPJ2