Question

find the solution in given picture​

Answer 1

Answer:

A=44,B=108andC=28

Step-by-step explanation:

Sum of all angles of a triangle =180

(2x+20)+(4x+60)+(4x-20)=180

2x+20+4x+60+4x-60=180

2x+4x+4x+20+60-20=180

10x+80-20=180

10x+60=180

10x=180-60

10x=120

x=120÷10

x=12

Angle A=2x+20

=2×12+20

=24+20

=44

Angle B=4x+60

=4×12+60

=48+60

=108

Angle C=4x-20

=4×12-20

=48-20

=28

check :-

sum of all angle of a triangle =180

44+108+28=180

complete

Answer 2

Answer :-

• The value of x is 12°.
• The angles are 44°, 108° and 28°.

Given :-

• The angles of a triangle are (2x + 20)°, (4x + 60)° and (4x - 20)°.

To find :-

• The value of x and all the angles.

Step-by-step explanation :-

Detailed explanation of the solution :-

Let's understand!

We know the value of all the angles of a triangle with variables. We have to find the value of x by forming an equation with the given information.

How to solve?

We know that :-

Sum of all the angles in a triangle = 180°.

We will solve the sum using this property.

Calculations :-

Since all the angles in a triangle add up to 180°, therefore, these angles must also be equal to 180°.

Therefore, we get :-

$\sf(2x + 20)^{\circ} + (4x + 60)^{\circ} + (4x - 20)^{\circ} = 180^{\circ}$

Removing the brackets,

$\sf2x + 20^{\circ} + 4x + 60^{\circ} + 4x - 20^{\circ} = 180^{\circ}$

Putting the variables and the constants separately in brackets,

$\sf(2x + 4x + 4x) + (20 + 60 - 20)^{\circ} = 180^{\circ}$

On simplifying,

$\sf10x + 60^{\circ} = 180^{\circ}$

Transposing 60° from LHS to RHS, changing it's sign,

$\sf10x = 180^{\circ} - 60^{\circ}$

On simplifying,

$\sf10x = 120^{\circ}$

Transposing 10 from LHS to RHS, changing it's sign,

$\sf x = \dfrac{120^{\circ}}{10}$

Dividing 120 by 10,

$\sf x = 12^{\circ}.$

So, the value of x = 12°.

Therefore, the value of the angles are as follows :-

2x + 20° = 2 × 12° + 20° = 24° + 20° = 44°.

4x + 60° = 4 × 12° + 60° = 48° + 60° = 108°.

4x - 20° = 4 × 12° - 20° = 48° - 20° = 28°.

Thus, the angles are 44°, 108° and 28° respectively.

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Verification :-

To check our answer, let's add the value of the angles and see whether we get 180°.

44° + 108° + 28° = 180°.

Since the angles add up to 180°,

Hence verified!

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