Question

-The angles ofa quadrilateral are in
the realto of 2:3:5:8 rend the
measure of each angle
angle.​

Answer 1

Step-by-step explanation:

ratio of angles is 2:5:5:8

by taking x as a common factor between them we can name the angles

angleA =2x°--(1)

angleB=5x°---(2)

angleC=5x°---(3)

angleD=8x°---(4)

we know the sum of angles of an quadrilateral is 360°

therefore ,

angleA+angleB+angleC+angleC=360°

• 2x°+5x°+5x°+8x°=360°
• 20x°=360°
• x=360/20
• x=18

substitute the value of x in eqn (1)(2)(3)and(4) we get

angleA=36°

angleB=90°

angleC=90°

angleD=144°

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Answer 2

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

⟹ The angles of the quadrilateral are in the ratio of 2:3:5:8

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

⟹ Measure of each angle = ?

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

$\sf \bigstar \: \underline{ Let \: us \: assume \: that},$

$\implies \sf First \: angle \: be \: 2x$

$\implies \sf Second \: angle \: be \: 3x$

$\implies \sf Third \: angle \: be \: 5x$

$\implies \sf Fourth \: angle \: be \: 8x$

$\bf Now,$

$\sf \dashrightarrow \underline{ \boxed{ \sf Sum \: of \: the \: interior \: angles \: of \: quadrilateral = 360 ^ \circ}}$

$\bf So,$

$\implies \sf 2x + 3x + 5x + 8x = 360^ \circ$

$\implies \sf 18x = 360^ \circ$

$\implies \sf x = \dfrac{360^ \circ}{18}$

$\implies \sf x = 20^ \circ$

$\implies \sf {Value \: of \: x \: is \: 20^ \circ }$

$\bf Now,$

$\sf \bigstar \: \underline{ Angles \: of \: quadrilateral \: are : }$

$\sf \implies First \: angle \: (2x) = 2 \times 20^ \circ = 40^ \circ$

$\sf \implies Second \: angle \: (3x) = 3 \times 20^ \circ = 60^ \circ$

$\sf \implies Third \: angle \: (5x) = 5\times 20^ \circ = 100^ \circ$

$\sf \implies Fourth \: angle \: (8x) = 8\times 20^ \circ = 160^ \circ$

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

$\implies \sf 2x + 3x + 5x + 8x = 360^ \circ$

$\sf \implies 2 \times 20^ \circ + 3 \times 20^ \circ + 5 \times 20^ \circ + 8 \times 20^ \circ = 360^ \circ$

$\sf \implies 40^ \circ + 60^ \circ + 100^ \circ + 160^ \circ = 360^ \circ$

$\sf \implies 360^ \circ = 360^ \circ$

$\sf \implies LHS = RHS$

$\bf Hence\:verified \:!!$