Mathematics
The angles of a quadrilateral are in the ratio 3 : 5 : 7. If the difference between the largest and the smallest of these angles is 76°; find the fourth angle of the quadrilateral.
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Answer
It is given that the angles of a quadrilateral are in the ratio 3 : 5 : 7.
Let the three angles of the quadrilateral be 3a, 5a and 7a.
The difference between the largest and the smallest of these angles is 76°.
Largest angle = 7a
Smallest angle = 3a
So,
⇒ 7a - 3a = 76°
⇒ 4a = 76°
⇒ a =
⇒ a = 19°
Three angles are 3a, 5a and 7a
⇒ 3 x 19°, 5 x 19° and 7 x 19°
⇒ 57°, 95° and 133°
As we know, the sum of all angles of quadrilateral is 360°.
⇒ 57° + 95° + 133° + x° = 360°
⇒ 285° + x° = 360°
⇒ x° = 360° - 285°
⇒ x° = 75°
Hence, the fourth angle is 75°.
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