Two angles of a quadrilateral are $68^{o}$ and $76^{o}$ . If the other two angles are in the ratio 5 : 7; find the measure of each of them.

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Solution

Two angles are $68^{o} a n d 76^{o}$

Let other two angles be 5x and 7x

$∴ 68^{o} + 76^{o} + 5 x + 7 x = 360^{o} 12 x + 144^{o} = 360^{o} 12 x = 360^{o} - 144^{o} 12 x = 216^{o} x = 18^{o}$

$∴$ angle are 5x and 7x

i.e. $5 \times 18^{o} a n d 7 \times 18^{o} i . e . 90^{o} a n d 126^{o}$

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Two angles of a quadrilateral are 68o and 76o. If the other two angles are in the ratio 5 : 7; find the measure of each of them.

Two angles are 68o and 76o Let other two angles be 5x and 7x ∴68o+76o+5x+7x=360o12x+144o=360o12x=360o−144o12x=216ox=18o ∴ angle are 5x and 7x i.e. 5×18o and 7×18o i.e.90o and 126o

Two angles of a quadrilateral are $68^{o}$ and $76^{o}$ . If the other two angles are in the ratio 5 : 7; find the measure of each of them.

Two angles are $68^{o} a n d 76^{o}$

Let other two angles be 5x and 7x

$∴ 68^{o} + 76^{o} + 5 x + 7 x = 360^{o} 12 x + 144^{o} = 360^{o} 12 x = 360^{o} - 144^{o} 12 x = 216^{o} x = 18^{o}$

$∴$ angle are 5x and 7x

i.e. $5 \times 18^{o} a n d 7 \times 18^{o} i . e . 90^{o} a n d 126^{o}$