The angles of a quadrilateral are in the ratio of 1:2:3:4. What is the measure of the four angles?​

2 thoughts on “The angles of a quadrilateral are in the ratio of 1:2:3:4. What is the measure of the four angles?​”

1. Question:

   The angles of a Quadrilateral are in the ratio of [tex]1:2:3:4 [/tex]. What is the measure of the four angles?

   Given-:

   Ratios of four angles of quadrilateral are [tex]1:2:3:4 [/tex]

   Answer:

   Let the angles of quadrilateral be [tex]x,2x,3x\: and\: 4x [/tex]

   We know, sum of all angles of quadrilateral is [tex]360° [/tex]

   [tex]\therefore [/tex] [tex]x+2x+3x+4x=360° [/tex]

   [tex]\implies [/tex] [tex]10x=360° [/tex]

   [tex]\implies [/tex] [tex]x=[/tex] [tex]\large\cancel\frac{360}{10} [/tex]

   [tex]\underline\color{purple}\boxed{x=36°} [/tex]

   Final Answer

   Angles are

   [tex]1x=36×1=36[/tex]

   [tex]2x=36×2=72 [/tex]

   [tex]3x=36×3=108 [/tex]

   [tex]4x=36×4=144 [/tex]

   Hence, the angles are [tex]36,72,108\: and\: 144 [/tex]

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2. Answer:

   the measure of all 4 angles are – 36 , 72 , 108 , 144.

   Step-by-step explanation:

   let the angles of a quadriletral be 1x, 2x,3x,and 4x

   applying angle sum property of quadriletral ( measure 360)

   1x + 2x +3x +4x = 360°

   10x = 360

   x = 360/10

   x= 36

   value of x = 36

   applying the value of x in each

   1x = 1*36 =36

   2x = 2*36= 72

   3x = 3*36 = 108

   4x = 4*36 = 144

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