Question

12. If the angles of a quadrilateral are x, x + 30°,
2x - 30° and 2x, then the greatest angle is
(a) 136 (b) 90° (c) 60° (d) 120°
a regular​

Answer 1

Answer:

120

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Answer 2

Correct Question :-

If the angles of a quadrilateral are x, x + 30°,2x - 30° and 2x, then the greatest angle is

(a) 136° (b) 90° (c) 60° (d) 120°

Solution :-

$\large{ \sf{ \underline{ We \: know :-}}}$

$\small{ \boxed{ \purple{ \sf{angle \: sum \: property \: of \: quadrilateral = {360}^{o}}}}}$

$\large{ \sf{ \underline{ Given :-}}}$

Let the angles be x°, x + 30°,2x - 30° and 2x°

$\large{ \sf{ \underline{ Now :-}}}$

$\small{ \sf{ \implies{x + x + 30 + 2x - 30 + 2x = {360}^{o} }}}$

$\small{ \sf{ \implies{6x = {360}^{o} }}}$

$\small{ \sf{ \implies{x = \frac{360}{6} }}}$

$\small{ \sf{ \implies{x = {60}^{o} }}}$

$\large{ \sf{ \underline{So :- }}}$

$\small{ \sf{ \purple{ \implies \: {x = {60}^{o} }}}}$

$\small{ \sf{ \purple{ \implies \: {x + 30 = {60 + 30 = {90}^{o} }}}}}$

$\small{ \sf{ \purple{ \implies \: {2x + 30 = {2 \times 60 - 30 = {90}^{o} }}}}}$

$\small{ \sf{ \purple{ \implies\: {2x = 2 \times 60 = {120}^{o}}}}}$

$\large{ \boxed{ \red{ \sf{ \therefore{greatest \: angle = {120}^{o} }}}}}$

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Verification :-

$\small{ \boxed{ \purple{ \sf{angle \: sum \: property \: of \: quadrilateral = {360}^{o}}}}}$

$\small{ \sf{ \implies{60 + 90 + 90 + 120 = {360}^{o} }}}$

$\large{ \sf{ \therefore{ Hence \: proved }}}$

__________________________

MARK BRAINLIEST ♡