The four angles of a quadrilateral are as $3 : 5 : 7 : 9$ . Find the angles

45^{o}, 75^{o}, 105^{o}, 135^{o}

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45^{o}, 75^{o}, 105^{o}, 140^{o}

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45^{o}, 75^{o}, 110^{o}, 135^{o}

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45^{o}, 70^{o}, 105^{o}, 135^{o}

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Solution

The correct option is A $45^{o}, 75^{o}, 105^{o}, 135^{o}$
The four angles of a quadrilateral are as $3 : 5 : 7 : 9$ .
Let angles are $3 x, 5 x, 7 x, a n d 9 x$
$3 x + 5 x + 7 x + 9 x = 360$
=> $24 x = 360$
=> $x = 15$
Angles are $3 \times 15 = 45^{o}, 5 \times 15 = 75^{o}, 7 \times 15 = 105^{o}, 9 \times 15 = 135^{o}$

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Similar questions

If two angles of a quadrilateral are 45^o and 75^o, sum of the other two angles is _____ .

90^{o}, 135^{o}, 45^{o}

∠ A = 45^{o}, ∠ B = 75^{o}

a + c \sqrt{2} = 2 b

P Q R S

P Q = 4.7 c m, Q R = 3.9 c m, ∠ Q P S = 75^{o}, ∠ P Q R = 120^{o}

∠ Q R S = 105^{o}

∠ P S R

\frac{1 + \sqrt{3}}{sin A} = \frac{2}{sin B} = \frac{\sqrt{6}}{sin 60^{o}}

∠ A = 75^{o}, ∠ B = 45^{o}

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