Question

ABCD is a cyclic quadrilateral. mLA = 14x+25)° and mLC =(5x+20)
Find the value of x and mLc.
(1) 15; 75°
(2) 15: 80° (3) 15: 85 (4) 15; 95°
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Answer 1

Answer:

Opposite angle in cyclic have sum 180°

So,

angle A + angle C = 180°

4x + 25 + 5x + 20 = 180°

9x + 45 = 180°

9x = 180° - 45°

9x = 135°

x = 135°/ 9

x = 15°

So, angle C = 5x + 20 = 75 + 20 = 95°

Answer 2

Explanation:

Opposite angle in cyclic have sum 180°

So,

angle A + angle C = 180°

4x + 25 + 5x + 20 = 180°

9x + 45 = 180°

9x = 180° - 45°

9x = 135°

x = 135°/ 9

x = 15°

So, angle C = 5x + 20 = 75 + 20 = 95°