Question

The measures of angles of a triangle are xº, (x-20)º,(x-40)º, find x ​

Answer 1

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$\underline{\textbf{\textsf{\orange{Solution:}}}}$

$\: \large \red {\bold{ \underline{ \: step \: by \: step \: explaination : }}}$

$\bullet \bf{ \: sum \: of \: sides \: of \: triangle = 180 \degree}$

$\: \underline{\bf{according \: to \: given \: conditions}}$

$\implies\displaystyle\sf{ \angle A+\angle B+\angle C=180 \degree}$

$\\ \implies \displaystyle \sf \: x \degree + (x - 20) \degree + (x - 40) \degree = 180 \degree$

$\: \implies \displaystyle \sf \: 3x \degree \: - 60 \degree = 180 \degree$

$\: \: \implies \displaystyle \sf \: 3x \degree - 60 \degree- 180 \degree = 0$

$\: \: \implies \displaystyle \sf \: 3x \degree = 240 \degree$

$\: \: \implies \displaystyle \sf \: x \degree = \frac{240}{3} = 80 \degree$

$\implies\displaystyle\sf{ \angle A= x\degree=80\degree}$

$\implies\displaystyle\sf{\angle B=(x-20)\degree=(80-20)\degree=60\degree}$

$\implies\displaystyle\sf{\angle C=(x-40)\degree=(80-40)\degree=40\degree}$

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Answer 2

By Angle sum property of a triangle,
x + (x-20)+(x-40) = 180
=> x + x - 20 + x - 40 = 180
=> 3x - 60 = 180
=> 3x = 180 + 60
=> x= 240 / 3
=> x = 80
and we got it!