1. Find the value of the unknown in each of the following figures.
2. Two of the interior angles of an n-sided polygon are 74 and 136°, and the remaining interior angles are 110 each. Find the value of n.
please help me :(
Answers
Sum of internal angles of n sided polygon = (n-2)×180°.
1. Figure-a:
Total sides, n = 5
Sum of internal angles = (5-2) × 180 = 3×180 = 540°
Adding the given angles, 107 + a + a + 121 + a = 540
⇒ 3a + 228 = 540
⇒ 3a = 540 - 228 = 312
⇒ a = 312/3
⇒ a = 104
Similarly, in Figure-b:
Total sides, n = 6
Sum of internal angles = (6-2) × 180 = 4×180 = 720°
Adding the given angles, 128 + 114 + 104 + 4b + 3b + 122 = 720
⇒ 7b + 468 = 720
⇒ 7b = 720 - 468 = 252
⇒ b = 252/7
⇒ b = 36
2. Two of the interior angles of an n-sided polygon are 74 and 136°, and the remaining interior angles are 110 each.
Sum of angles = 74 + 136 + (n-2)×110
But we know that, Sum of angles = (n-2)×180
Thus, 74 + 136 + (n-2)×110 = (n-2)×180
⇒ 210 + 110n - 220 = 180n - 360
⇒ 110n - 180n = -360 + 220 - 210
⇒ -70n = -350
⇒ n = 350/70
⇒ n = 5
please check the attached file
