If the three angles of a triangle are (x + 15°), (6x/5+6) and (2x/3+30),prove that the triangle is an equilateral triangle.
Answers
Answer:
Hope my answer helps you mate :-)
Step-by-step explanation:
It is obvious that a is being formed.
So by Angle sum property
x+15+6x/5+6+2x/3+30=180
x+6x/5+2x/3=129
15x+18x+10x/15=129
43x=129×15
x=3×15=45
so put this value in given value
60,60 and 60 respectively
so as all angke are 60 and equal we can say it is equilateral as equiangular
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Answer:
Each angle = 60°
Step-by-step explanation:
Given a triangle.
The angles are given in Variable terms as
- (x+15)°
- (6x/5+6)°
- (2x/3+30)°
To prove that it's an equilateral triangle.
By angle sum property of a traingle,
We know that,
Sum of angles = 180°
Therefore, we will get,
=> x+15+6x/5+6+2x/3+30 = 180°
=> (x+6x/5+2x/3) + (15+6+30) = 180
=> {(15x+18x+10x)/15} + 51 = 180
=> 43x/15 = 180-51
=> 43x/15 = 129
=> x = 129 × 15/43
=> x = 3 × 15
=> x = 45
Therefore, we get,
=> x+15 = 45+15 = 60°
=> 6x/5+6 = 6(45)/5+6 = 54+6 = 60°
=> 2x/3+30 = 2(45)/3+30 = 30+30 = 60°
Since, all the angles measure 60°.
Hence, it's an equilateral triangle.
Thus, proved.