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Angle 'A' of the quadrilateral ABCD is \( \Large 26^{\circ} \) less than angle B. Angle B is twice angle C and angle C is \( \Large 10^{\circ} \) more than the angle D. What would be the measure of angle A ?


A) \( \Large 104 ^{\circ} \)

B) \( \Large 126 ^{\circ} \)

C) \( \Large 56 ^{\circ} \)

D) \( \Large 106 ^{\circ} \)

Correct Answer:
D) \( \Large 106 ^{\circ} \)

Description for Correct answer:
Let \( \Large \angle A = x \)

\( \Large \therefore \angle B = x + 26 \)

\( \Large \angle C = \frac{x + 26}{2} = \frac{x}{2} + 13 \)

\( \Large \angle D = \frac{x}{2} + 3 \)

\( \Large \therefore x + x + 26 + \frac{x}{2} + 13 + \frac{x}{2} + 3 \)

= \( \Large 360 ^{\circ} \)

=> \( \Large 3x = 360 - 42 = 318^{\circ} \)

=> \( \Large x = \frac{318}{3} = 106 ^{\circ} \)

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