Question

ABCD is a parallelogram; angle A=(5b+6)°; angle B=(4a-8)°;angle C=(8a-10)°.Find the value of a

and b.Also find angle D.



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Answer 1

GIVEN :-

• ABCD is parallelogram.
• Angle A = (5b+6)°
• Angle B = (4a-8)°
• Angle C = (8a-10)°

TO FIND :-

• Value of a and b.
• Angle D.

SOLUTION :-

As ABCD is parallelogram , opposite angles are equal and adjacent angles are supplementary(sum is 180°).

Angle B and Angle C are supplementary. Hence , sum is 180°.

→ 4a - 8 + 8a - 10 = 180

→ 12a - 18 = 180

→ 12a = 180 + 18

→ 12a = 198

→ a = 198/12

→ a = 16.5

Angle A and Angle B are supplementary. Hence , sum is 180°.

→ 5b + 6 + 4a - 8 = 180

→ 5b - 2 + 4a = 180

→ 5b + 4a = 180 + 2

→ 5b + 4a = 182

Putting a = 16.5,

→ 5b + 4(16.5) = 182

→ 5b + 66 = 182

→ 5b = 182 - 66

→ 5b = 114

→ b = 114/5

→ b = 22.8

__________________

Angle B = 4a - 8

Angle B = 4(16.5) - 8

Angle B = 66 - 8

Angle B = 58°

Since , Angle B and Angle D are opposite angles , Angle B = Angle D

Therefore , Angle D = 58° , a = 16.5 , b = 22.8