Question

In a quadrilateral ABCD, the angle A B C and D are in ratio 1 :2: 3 : 4 . find the measure of each angle of the quadrilateral​

Answer 1

Step-by-step explanation:

Let the angles of quadrilateral be x,2x,3x and 4x

The sum of all angles=180⁰

Therefore, x+2x+3x+4x=180⁰

10x=180⁰

x=180/10

x=18⁰

x=18⁰, 2x=18×2 , 3x=18×3 , 4x=18×4

=36⁰ =54⁰ =72

Answer 2

$\large\underline{ \underline{ \sf \maltese{ \: Question:- }}}$

• In a quadrilateral ABCD, the angle A B C and D are in ratio 1 :2: 3 : 4 . find the measure of each angle of the quadrilateral

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

$\red{\boxed{ \sf \blue{ \angle{A}\:: \angle{B} \:: \angle{C}\:: \angle{D}\: = \: 1:2:3:4 }}}$

• $\sf\green{Let \: \angle{A}\: = \blue{\fbox\orange{x }} }$
• $\sf\green{Let \: \angle{B}\: = \blue{\fbox\orange{2x }} }$
• $\sf\green{Let \: \angle{C}\: = \blue{\fbox\orange{3x }} }$
• $\sf\green{Let \: \angle{D}\: = \blue{\fbox\orange{4x}} }$

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

$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: \angle{A}\: + \: \angle{B} \: + \: \angle{C}\: + \: \angle{D}\: = \: 360 }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ x \: + \: 2x \: + \: 3x \: + 4x \: = \: 360 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 10x \: = \: 360 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ x \: = \:\frac{ 360}{10} }}$

$\qquad \quad {:}\longrightarrow\sf{\sf{x \: = \: \frac{36\cancel{0}}{1\cancel{0}} }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{x \: = \: 36 }}}$

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Measures of Angles:-

• ∠A = x = $\green{\fbox\purple{\:36° }}$
• ∠B = 2x = 2 × 36 = $\green{\fbox\purple{\:72° }}$
• ∠C = 3x = 3 × 36 = $\green{\fbox\purple{\:108° }}$
• ∠D = 4x = 4 × 36 = $\green{\fbox\purple{\:144° }}$

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

$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: \angle{A}\: + \: \angle{B} \: + \: \angle{C}\: + \: \angle{D}\: = \: 360 }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

$\qquad \quad {:} \longrightarrow \sf{\sf{36 \: + \: 72 \: + \: 108 \: + \: 144\: = \: 360 }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{360° \: = \: 360° }}}$

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$\bf \therefore \; ∠ \; A = 36°$

$\bf \therefore \; ∠ \; B = 72°$

$\bf \therefore \; ∠ \; C = 108°$

$\bf \therefore \; ∠ \; D = 144°$

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