Question

The measures of angles of a triangle are x°, (x- 20)°, (x- 40)°. Find x= ?​

Answer 1

Answer:

The value of x is 80°.

Step-by-step-explanation:

We have given that x°. ( x - 20 )° and ( x - 40 )° are the measures of angles of a triangle.

We have to find the value of x.

Now, we know that,

The sum of measures of angles of a triangle is 180°.

∴ x° + ( x - 20 )° + ( x - 40 )° = 180°

⇒ x + x - 20 + x - 40 = 180

⇒ x + x + x - 20 - 40 = 180

⇒ 3x - 60 = 180

⇒ 3x = 180 + 60

⇒ 3x = 240

⇒ x = 240 ÷ 3

⇒ x = 80°

∴ The value of x is 80°.

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Verification:

First angle = x = 80°

Second angle = ( x - 20 ) = ( 80 - 20 ) = 60°

Third angle = ( x - 40 ) = ( 80 - 40 ) = 40°

Now, by angle sum property of triangle,

80° + 60° + 40° = 180°

⇒ 140 + 40 = 180

⇒ 180° = 180°

Hence verified!

Answer 2

Given :-

• Measures of Angle of triangle are
• x° , (x - 20)° , (x - 40°)

To find :-

• Value of x

We know that :-

• Sum of all angles of triangle is 180°.

${ \bigstar{ \sf{ \: So, according \: \: to \: \: the \: \: question :- }}}$

${\mathtt{\implies{x° + (x - 20°) + (x - 40°) = 180° }}}$

${\mathtt{\implies{x° + x - 20° + x - 40° = 180 \degree}}}$

${\mathtt{\implies{x + x + x -20° - 40° = 180° }}}$

${\mathtt{\implies{3 x - 60° = 180° }}}$

${\mathtt{\implies{3x = 180° + 60}}}$

${\mathtt{\implies{3x = 240}}}$

${\mathtt{\implies{x = \frac{240}{3} }}}$

${ \large{ \color{green}{\mathtt{\implies{x = 80 \degree}}}}}$

So, value of x is 80°.

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For more finding all angles :-

Putting the value of x ,

x = 80°

x - 20 = 80 - 20 = 60°

x - 40° = 80 - 40 = 40°

Verification :-

By angle sum property of triangle which states that sum of all angle of triangle is 180°.

= 80° + 60° + 40° = 180°

= 80° + 100° = 180°

= 180° = 180°

So, LHS = RHS

Hence, our answer 80° is correct answer.