Answer:
A = 42°
Step-by-step explanation:
Sum of all interior angles of a n -gon (n - sided figure) is (n - 2)180°.
Here the polygon is Seven sided so, n = 7.
Therefore, sum of all the interior angles should be (7 - 2)180° = 900°.
⇒ ∠A + ∠B + ∠C + ∠D + ∠E + ∠F + ∠G = 900°.
⇒ (9x - 2)° + (10x + 2)° + 165° + 100° + (5x + 83)° + (12x + 18)° + 138° = 900°.
Simplifying we get, 36x + 504° = 900°
⇒ 36x = 396
⇒ x = 16
Now substituting for x in ∠A = (9(16) - 2)°
⇒ ∠A = 142°
