Question

The measure of angles of triangle are x°, (x - 20)°and (x - 40°). Find x. *
1 point
100°
70°
90°
80°​

Answer 1

GIVEN :-

The measure of angles of triangle are x°, (x - 20)°and (x - 40)°.

TO FIND :-

The value of x.

SOLUTION :-

By using angle sum property of triangle we have,

$\begin{gathered}\\ : \implies \displaystyle \sf \: x ^{ \circ} + (x - 20) ^{ \circ} + (x - 40) ^{ \circ} = 180 ^{ \circ} \\ \\ \\\end{gathered}$

$</p><p>\begin{gathered}: \implies \displaystyle \sf \: x ^{ \circ} + x - 20 ^{ \circ} + x - 40 ^{ \circ} = 180 ^{ \circ} \\ \\ \\\end{gathered}$

$\begin{gathered}: \implies \displaystyle \sf \:3x - 60 = 180 ^{ \circ} \\ \\ \\\end{gathered}$

$</p><p>\begin{gathered}: \implies \displaystyle \sf \:3x = 180 ^{ \circ} + 60 ^{ \circ} \\ \\ \\\end{gathered}$

$\begin{gathered}: \implies \displaystyle \sf \:3x = 240 ^{ \circ} \\ \\ \\\end{gathered} </p><p>$

$</p><p>\begin{gathered}: \implies \displaystyle \sf \:x = \frac{240 ^{ \circ} }{3} \\ \\ \\\end{gathered} </p><p>$

$\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \: \bold{x = 80 ^{ \circ} }}} \\ \\\end{gathered}$

• Hence the required value of x is 80°.

Answer 2

Given :

The measure of angles of triangle are

a = x°

b = (x - 20)°

c = (x - 40)°

To Find :

The value of x

Solution :

By angle sum property of triangle,

a + b + c = 180°

$\sf \implies x° + (x - 20)° + (x - 40)° = 180°$

$\sf \implies x° + x° - 20° + x° - 40° = 180°$

$\sf \implies 3x° - 60° = 180°$

$\sf \implies 3x° = 180° + 60°$

$\sf \implies 3x° = 240°$

$\sf \implies x° = \dfrac{240°}{3}$

$\sf \implies x° = \dfrac{\cancel{240°}^{80°}}{\cancel{3}_{1}}$

$\sf \implies x° = 80°$

$\boxed{\sf x = 80°}$

Therefore, value of x = 80°