Question

three angles of a quadrilateral are in the ratio 3 ratio 4 ratio 5 the difference of the least and the greatest of the angles is 45 degree. find all the four angles of the quadrilateral​

Answer 1

QUESTION:

three angles of a quadrilateral are in the ratio 3 ratio 4 ratio 5 the difference of the least and the greatest of the angles is 45 degree. find all the four angles of the quadrilateral

SOLUTION IN IMAGE

Given the difference of the least and the greatest of the angles is 45 degree

PUT IN EQUATION

SOLVE AND FIND VALUE OF "X"

ASSIGN"X" TO THE OTHER RATIOS AND SOLVE

Answer 2

⇝Given :-

• Ratios = 3:4:5
• Difference between latgest and smallest angle = 45°

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⇝To Find :-

• Find all the 4 angles .

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⇝We know that :

${\orange{\bigstar{\underline{\green{\text{Sum of all angles of a quadrilateral is 360°}}}}}}$

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⇝Solution :-

❒ Let :

${\red{\rightarrowtail}{\bf{1st \: angle = 3x}}}$

${\red{\rightarrowtail}{\bf{2nd \: angle = 4x}}}$

${\red{\rightarrowtail}{\bf{3rd \: angle = 5x}}}$

${\red{\rightarrowtail}{\bf{4th \: angle = y}}}$

❒ Value of x as we have been given difference between smallest and largest angle is 45° :

${\large{:{\longmapsto{\bf{5x - 3x = 45°}}}}}$

${\large{:{\longmapsto{\bf{2x = 45°}}}}}$

${\large{:{\longmapsto{\bf{x = {\cancel \frac{45}{2} }}}}}}$

${\orange{\large{:{\dashrightarrow{\underline{\blue{\bf{X = 22.5}}}}}}}}$

❒ 3 angles are :

${\mapsto{\bf{\pink{1st \: angle = 3 \times 22.5 = 67.5°}}}}$

${\mapsto{\bf{\pink{2nd \: angle = 4 \times 22.5 = 90°}}}}$

${\mapsto{\bf{\pink{3rd \: angle = 5 \times 22.5 = 112.5°}}}}$

❒ Now 4th angle :

${\large{:{\longmapsto{\bf{Sum \: of \: all \: angles \: of \: quadrilateral = 360°}}}}}$

${\large{:{\longmapsto{\bf{ \: \: \: \: \: \: 67.5° + 90° + 112.5° + y= 360°}}}}}$

${\large{:{\longmapsto{\bf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 270 + y= 360°}}}}}$

${\large{:{\longmapsto{\bf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: y= 360 - 270}}}}}$

${\large{:{\longmapsto{\bf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {y = 90°}}}}}$

❒ Hence :

${\large{:{\leadsto{\bf{\red{1st \: angle = 67.5°}}}}}}$

${\large{:{\leadsto{\bf{\red{2nd \: angle = 90°}}}}}}$

${\large{:{\leadsto{\bf{\red{3rd \: angle = 112.5°}}}}}}$

${\large{:{\leadsto{\bf{\red{4th \: angle = 90°}}}}}}$

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