Mathematics
The angles of a quadrilateral are in A.P. with common difference 20°. Find its angles.
AP
52 Likes
Answer
Let the angles of quadrilateral are,
a, a + d, a + 2d, a + 3d
∴ a + (a + d) + (a + 2d) + (a + 3d) = 360°
⇒ 4a + 6d = 360°
⇒ 2(2a + 3d) = 360°
⇒ 2a + 3d = 180°
Putting value of d = 20° in above equation we get,
⇒ 2a + 3(20) = 180°
⇒ 2a + 60 = 180°
⇒ 2a = 180° - 60 = 120°
⇒ a = 60°.
Hence, angles = 60°, 80°, 100°, 120°.
Answered By
34 Likes
Related Questions
If 5, 7 and 9 are in A.P. then which of the following is in A.P.?
5 × 7, 7 × 9 and 9 × 5
5 × 7, 7 × 7 and 9 × 7
2 × 5, 2 × 7 and 5 × 9
5 - 7, 7 - 9 and 9 - 5
Find three numbers in A.P. whose sum is 24 and whose product is 440.
Divide 96 into four parts which are in A.P. and the ratio between product of their means to product of their extremes is 15 : 7.
Find five numbers in A.P. whose sum is and the ratio of the first to the last term is 2 : 3.