Question

ratio 3:5: 7:9.
ABCD is a quadrilateral. AO and BO are the angle bisectors of angle A
and B which meet at O. If ZC=709, ZD = 50°, find angle AOB​

Answer 1

Answer:

In quadrilateral ABCD,

angle A + angle B + angle C + angle D = 360° (sum of all inner angles of a quadrilateral is 360°)

angle A = x + x (since AO bisects angle A)

angle B = y + y (since BO bisects angle B)

Therefore,

2x + 2y + 70° + 50° = 360°

2(x+y) + 130° = 360°

2(x+y) = 360° - 130° = 230°

x + y = 230/2 = 115° ---------- (i)

In triangle AOB,

x+y+angle AOB = 180° (Sum of all angles of a triangle is 180°)

115° + angle AOB = 180° ( eq.{i})

Therefore angle AOB = 180° - 115° = 65°

Step-by-step explanation:

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