Math, asked by ramyasebi211, 3 months ago

angle of a qudrilateral are in ratio 3x 4 x5x 6x ​

Answers

Answered by Nausiya
0

Step-by-step explanation:

Given that angles of a quadrilateral are in the ratio 3 : 4: 5 : 6 .Let the angle be 3x , 4x , 5x , 6x

3x+4x+5x+6x=360o

⇒x=18360o

⇒x=20o

Therefore the angles are

3×20=60o

4×20=80o

5×20=100o

6×20=120o

Since all the angles are different degrees thus from as trapezium

Answered by ItzShinyQueenn
2

  \mathbb{\underline{ \underline{Given:- }}}

• \:  \sf{Angle  \: of  \: a \:  qudrilateral  \: are  \: in  \: ratio  \: 3: 4 : 5 : 6 }

  \mathbb{\underline{ \underline{To \:  Find :- }}}

 \sf• \: The \:  angles \:  of  \: the \:  quadrilateral.

  \mathbb{\underline{ \underline{ Solution :-}}}

 \sf Let \:  the \:  constant \:  be  \: x

 \sf{So, \:  the \:  angles \:  are  \: respectively \: 3x \: , 4x \: ,5x \: ,6x \: .}

 \sf{We  \: know \:  that,  \: the  \: sum \:  of \:  the  \: four \:  angles  \: of  \: a \:  quadrilateral  \: is  \: 360°.}

 \sf{According  \: to \:  the \:  question,  }

 \sf3x + 4x + 5x + 6x = 360 \degree

 \sf⇒18x = 360 \degree

 \sf⇒ x=  \frac{360 \degree}{18}

 \sf⇒x = 20 \degree

 \therefore \sf1st \:  angle =( 3 \times 20) \degree = 60 \degree

 \therefore \sf2nd  \: angle =( 4 \times 20) \degree = 80 \degree

 \therefore \sf3rd  \: angle =( 5\times 20) \degree =10 0 \degree

 \therefore \sf4th  \: angle  =( 6\times 20) \degree =12 0 \degree

 \sf \red{Hence,  \: the  \: angles  \: of  \: the \:  quadrilateral  \: are \:  respectively }  \\  \sf \red{60°, 80°, 100° \:  and  \:  \: 120°.}

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