Question

If the angles of a triangle measures (x+40)⁰,(2x+20)⁰ and 3x⁰,find all the angles of a triangle. Also state which type of triangle is this. and
answer should be :- 60⁰,60⁰,60⁰; acute - angled triangle; pls answer it step by step​

Answer 1

Step-by-step explanation:

Given:-

the angles of a triangle measures (x+40)⁰,(2x+20)⁰ and 3x⁰

To find:-

Find all the angles of a triangle.

Solution:-

Given that:

The angles of a triangle are

(x+40)°

(2x+20)°

3x°

We know that

"The sum of all angles in a triangle is equal to 180°".

=>(x+40)° + (2x+20)° + 3x° = 180°

=>(x°+2x°+3x°) + (40°+20°) = 180°

=>6x° + 60° = 180°

=>6x° = 180° - 60°

=>6x° = 120°

=> x° = 120°/6

=>x° = 20°

The value of x°= 20°

Now,

The value of (x+40)°= 20°+40° = 60°

The value of (2x+20)° = 2(20°)+20° = 40°+20°=60°

The value of 3x° = 3(20°)=60°

Answer :-

The angles of the given triangle are

60° , 60° , 60°

The triangle is an acute angled triangle.

Since each angle is less than 90°

Used formulae:-

• The sum of all angles in a triangle is 180°
• All angles are acute the triangle is called an acute angled triangle
• If an angle between 0° and 90° is called an acute angle
• In an equilateral triangle each angle is equal to 60°

Answer 2

Step-by-step explanation:

Let first angle be = x+40°

Second angle = 2x+20°

Third angle = 3x°

Since the sum of angles in a triangle = 180°

Therefore forming an equation

(x+40) + (2x+20) + 3x = 180

= x = 20

Therefore first angle = 20+40 = 60°

Second angle = 2×20+20 = 60°

Third angle = 3×20 = 60°

Therefore the triangle is an equilateral triangle as sum of the angles is 180°

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