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The angles of a quadrilateral are in AP whose common difference is $5 °$ . What will be the values of angles?

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80 °, 90 °, 95 ° and 105 °

70 °, 80 °, 90 ° and 110 °

75 °, 85 °, 95 ° and 105 °

65 °, 75 °, 85 ° and 9 5 °

answer is B.

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Detailed Solution

Given that the angle of a quadrilateral are in A.P. whose common difference is

5 °

.
The general arithmetic progression is

a − 3 d, a − d, a + d

and

a + 3 d

. We know that, the sum of all angles of a quadrilateral

= 360 °

.
Let the required angles are

(a − 15) °, (a − 5) °, (a + 5) °

and

(a + 15) °

.
Applying formula, we have,

∴ (a − 15) ° + (a − 5) ° + (a + 5) ° + (a + 15) ° = 360 ° ⇒ 4 a = 360 ° ⇒ a = 360 ° 4 ⇒ a = 90 °

Putting the value of

a = 90 °

in angles of quadrilateral:

∴ (90 − 15) °, (90 − 5) °, (90 + 5) ° and (90 + 15) ° ⇒ 75 °, 85 °, 95 ° and 105 °

Therefore, the required angles of a quadrilateral are

75 °, 85 °, 95 ° and 105 °

.
Hence, option (2) is correct.

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