The consecutive angle of a. trapezium form an arithmetic sequence, If the smallest is 75°, then the longest angle is

Class: 9

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110°

105°

110°

115°

answer is B.

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Detailed Solution

Sung angle of quadrilateral = 360°
∠ D = 75°, ∠ B = 75 + 2x, ∠ A = 75 + 3x, ∠ C = 75 + x
∠ A + ∠ B + ∠ C + ∠ D = 360°
75 + 3x + 75 + 2x + 75 + 8x + 75° = 360°
6x = 360 – 300
6x = 60
X = 10°
Largest angle = 75 + 3x
= 75 + 3 × 10
LA = 105°

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