Question

Find the measures of the four angles of a quadrilateral if they are in the ratio 3 : 5 : 7: 9.​

Answer 1

Answer:

Step-by-step explanation:

let the ratio be x

3x +5x + 7x + 9x = 360 degrees

24 x=360 degrees

x= 360/24 degrees

x = 15 degrees

3x = 3*15= 45 degrees

5x= 5*15= 75 degrees

7 x = 7 * 15 = 105 degrees

9x = 9*15 = 135 degrees.

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Answer 2

Answer:

Given :-

• The four angles of a quadrilateral are in the ratio of 3 : 5 : 7 : 9.

To Find :-

• What are the measures of the angles of a quadrilateral.

Solution :-

Let,

$\mapsto \bf First\: Angle_{(Quadrilateral)} =\: 3x$

$\mapsto \bf Second\: Angle_{(Quadrilateral)} =\: 5x$

$\mapsto \bf Third\: Angle_{(Quadrilateral)} =\: 7x$

$\mapsto \bf Fourth\: Angle_{(Quadrilateral)} =\: 9x$

As we know that :

$\footnotesize \bigstar \: \: \sf\boxed{\bold{\pink{Sum\: of\: all\: angles_{(Quadrilateral)} =\: 360^{\circ}}}}\: \: \: \bigstar$

According to the question by using the formula we get,

$\implies \sf 3x + 5x + 7x + 9x =\: 360^{\circ}$

$\implies \sf 8x + 16x =\: 360^{\circ}$

$\implies \sf 24x =\: 360^{\circ}$

$\implies \sf x =\: \dfrac{360^{\circ}}{24}$

$\implies \sf\bold{\purple{x =\: 15^{\circ}}}$

Hence, the required angles of a quadrilateral are :

$\small \dashrightarrow \sf\bold{\red{First\: Angle_{(Quadrilateral)} =\: 3x =\: 3 \times 15^{\circ} =\: 45^{\circ}}}$

$\small \dashrightarrow \sf\bold{\red{Second\: Angle_{(Quadrilateral)} =\: 5x =\: 5 \times 15^{\circ} =\: 75^{\circ}}}$

$\small \dashrightarrow \sf\bold{\red{Third\: Angle_{(Quadrilateral)} =\: 7x =\: 7 \times 15^{\circ} =\: 105^{\circ}}}$

$\small \dashrightarrow \sf\bold{\red{Fourth\: Angle_{(Quadrilateral)} =\: 9x =\: 9 \times 15^{\circ} =\: 135^{\circ}}}$

$\therefore$ The measure of all angles of a quadrilateral is 45° , 75° , 105° and 135° .