Question

Please someone solve this question​

Answer 1

Step-by-step explanation:

For the triangle being equilateral all the sides should be equal.....

Therefore, (x +15°) = (6x/5 + 6°) = (2x/3 + 30°)

x + 15 = 6x/5 + 6

x - 6x/5 = 6 - 15

x - 6x = - 9 × 5

-5x = - 45

x = - 45/-5

x = 9

2x/3 + 30 = 9

2x/3 = 9 - 30

2x = - 21 ×3

x = - 63/2 = - 31.5

Hence proved......

Hope this helps!!

Answer 2

Question :-

If the three angles of a triangle are ( x + 15° ) , ( 6x/5 + 6° ) & ( 2x/3 + 30° ) prove that the triangle is an equilateral triangle ?

A

Answer :-

Given :-

The three angles of a triangle are ( x + 15° ) , ( 6x/5 + 6° ) & ( 2x/3 + 30° )

Required to prove :-

• The triangle is an equilateral triangle

Conditions used :-

In a triangle , sum of all angles is equal to 180°

In an equilateral triangle the measures of 3 angles are equal because the all 3 sides are equal .

In an equilateral triangle , the measurement of each angle will be 60°

Solution :-

Given that :-

The three angles of a triangle are ( x + 15° ) , ( 6x/5 + 6° ) & ( 2x/3 + 30° )

we need to prove that the triangle is an equilateral triangle .

So,

Let's prove that the given triangle is an equilateral triangle .

Consider the given angles ;

( x + 15° ) , ( 6x/5 + 6° ) & ( 2x/3 + 30° )

Here,

x is an unknown value .

So, if we are able to find the value of x then we can easily prove that this triangle is an equilateral triangle .

Now,

Let's find the value of x ;

So,

we know that ;

In a triangle , sum of all angles is 180°

which implies ;

x + 15° + 6x/5 + 6° + 2x/3 + 30° = 180°

x + 6x/5 + 2x/3 + 15° + 6° + 30° = 180°

x + 6x/5 + 2x/3 + 51° = 180°

Transpose + 51° to the right side

x + 6x/5 + 2x/3 = 180° - 51°

x + 6x/5 + 2x/3 = 129°

Here we need to take LCM on the left side

LCM = 15

15x + 18x + 10x/15 = 129°

43x/15 = 129°

43x = 129° x 15

43x = 1935°

x = 1935°/43

x = 45°

Hence,

• Value of x = 45°

Now, let's find the measurement of each angle ;

=> x + 15° = 45° + 15° = 60°

=> 6x/5 + 6° = 6 x 45°/ 5 + 6° = 6 x 9° + 6° = 54° + 6° = 60°

=> 2x/3 + 30° = 2 x 45°/ 3 + 30° = 2 x 15° + 30° = 30°+30° = 60°

Hence,

The measurements of the three angles are ; 60° , 60° & 60°

Since, the measurements of the three angles is equal to 60° .

So,

we can conclude that ;

If an triangle has every angle equal to 60° then it is an equilateral triangle .

This implies ;

The given triangle is an equilateral triangle .

Hence proved !!