Question

if an angle of a parallelogram in two-third of its adjacent angle, find the angles of parallelogram.

Answer 1

Let ABCD is a paralelogram and angle A be x then, angle B will be 2/3x.
as we know that opposite angles are equal in paralelogram.
so, angle A is x then, angle C also will be x.
similarly B = C =2/3x.
A/Q
sum of all angles of paralelogram make 360°.
angles A + B + C + D = 360°.
x + 2/3x + x + 2/3x = 360°.
(3x + 2x + 3x + 2x)/3 = 360°
10x = 360° × 3
x = (360° × 3)/10
x = 36° × 3
x = 108°
Hence, angle A and C = x = 108°
and angle B and D = 2/3x = 2/3 × 108° = 2 × 36° = 72° Ans

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