Question

Measurement of the angles of a triangle are represented by (3×-20),(7×+30) and (2×+50) find x

Answer 1

$\bf \underline{ \underline{\maltese\:Given} }$

$\sf Measurement \: of \:the \:angles\: of \:a \:triangle \:are :$

$\sf \implies(3x-20) \: , \: (7x+30) \: ,\: (2x+50)$

$\bf \underline{\underline{\maltese\: To \: find }}$

$\sf \implies Value \: of \: x = \: ?$

$\bf \underline{\underline{\maltese\: Solution }}$

$\sf As \: we \: know \: that,$

$\underline{ \boxed{ \sf The \: sum \: of \: the \: three \: angles \: of \: triangle \: is= 180^{\circ} }}$

$\bf \underline{ Now},$

$\sf \implies(3x-20) \: + \: (7x+30) \: + \: (2x+50) = 180^{\circ}$

$\rm \underline{ Add \: 3x \: and \: 7x }$

$\sf \implies10x-20+30 \: + \: 2x+50= 180^{\circ}$

$\rm \underline{ Add \: 10x \: and \: 2x }$

$\sf \implies 12x-20+30 \: +50= 180^{\circ}$

$\rm \underline{ Simplify \: by \: adding \: numbers }$

$\sf \implies 12x+60 = 180^{\circ}$

$\sf \implies 12x= 180 - 60$

$\sf \implies 12x= 120$

$\sf \implies x= \cancel\dfrac{120}{12}$

$\sf \implies x= 10$

$\underline{\boxed{ \bf \red{Therefore, the \: value \: of \: x \: is \: 10.}} }$

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$\bf \underline{\underline{\maltese\: Verification }}$

$\sf \implies(3x-20) \: + \: (7x+30) \: + \: (2x+50) = 180^{\circ}$

$\rm \underline{ Write \: 10 \: instead \: of \: x }$

$\sf \implies(3 \times 10-20) \: + \: (7 \times 10+30) \: + \: (2 \times 10+50) = 180^{\circ}$

$\sf \implies(30-20) \: + \: (70+30) \: + \: (20+50) = 180^{\circ}$

$\sf \implies(10) \: + \: (100) \: + \: (70) = 180^{\circ}$

$\sf \implies10 + 100 + 70 = 180^{\circ}$

$\sf \implies180 = 180^{\circ}$

$\bf \underline{Hence \: verified \: ! }$