16) The angles of a quadrilateral are in AP, whose common difference is 10°. Find all of its four angles.

75°, 85°, 95°, 105°

Step-by-step explanation:

Since the 4 angles form an AP, then the 4 angles are

a, a + d, a + 2d, a + 3d

where a is the first term and d the common difference

The sum of the angles in a quadrilateral = 360° thus

a + a + d + a + 2d + a + 3d = 360, that is

4a + 6d = 360, substitute d = 10

4a + 60 = 360 ( subtract 60 from both sides )

4a = 300 ( divide both sides by 4 )

a = 75

Thus the 4 angles are

75°, 75° + 10° = 85°, 75° + 20 = 95°, 75° + 30° = 105°

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