Question

the opposite angles of a parallelogram are ( 3x-2) and ( x+ 48) . find the measure of each angle of the paralleolgram

Answer 1

Let four angles of given parallelogram taken in order be ∠A, ∠B, ∠C and ∠D respectively

Here opposite angles given ∠A = (3x - 2) and ∠C = (x + 48)

We know that opposite angles of a parallelogram are equal

∴ 3x - 2 = x + 48

2x = 50

x = 25

∴ 3x -2 = 73°

∠A  = ∠C = 73°

Also we know that sum of two adjacent angles of a parallelogram is 180

∴ ∠A + ∠B = 180°

73° + ∠B = 180°

∠B = 107° = ∠D (Opposite angles are equal)

∴ All four angles of given parallelogram are 73°, 107°, 73°, 107°

Answer 2

Answer:

in parallelogram,

opposite sides and angles are equal

3x-2=x+48

3x-x=48+2

2x=50

x=25

3x-2=(3 x 25) -2

3x-2=75-2

3x-2=73

therefore, x+48=73

by angle sum property , sum of all angles in a parallelogram is 360

73+73+y+y  (let the other opposite angles be y)

146+2y=360

2y= 214

y=214/2

y=107

therefore,

angles of parallelogram are 73,107,73,107