Question

An angle of a parallelogram is of measure 85. Find all the angles of the parallelogram.

● Give alternate method also.

Answer 1

given:ABCD is a parallelogram
angleA=85 degree
To find: all angles of parallelogram
solution: angleA=angleC =85 degree. (vertical opposite angles of a parallelogram are equal)
angleA+angleB=180 degree. (adjacent angles of a parallelogram are supplementary)
85 degree+angleB=180 degree
angleB=180 degree-85 degree
angle B = 95 degree
angle B=angleD=95 degree. (vertical opposite angles of a parallelogram are equal)
=) angle A=85 degree
angle B=95 degree
angle C=85 degree
angle D=95 degree

Answer 2

Let ABCD be a parallelogram with Angle A = 85°; Angle C = Angle A.

Angle A + Angle B + Angle C + Angle D = 360°

(Opposite angles of a parallelogram are equal)

85°+ Angle B + Angle 85°+ Angle D = 360°

Angle B + Angle D + 170° = 360°

(Angle sum property of a quadrilateral)

Angle B + Angle D = 360° - 170° = 190° .... (1)

But, Angle B = Angle D

(Opposite angles of a parallelogram are equal)

=》From Equation ( 1 )

Angle B + Angle B = 190°

2 Angle B = 190°

Angle B = 190°/2 = 95°

So, Angle B = Angle D = 95° and Angle A = Angle C = 85°


Thanks☺