Question

The opposite angles of a parallelogram are (3x - 2)° and (x +48)º
Find the measure of each angle of the parallelogram.​

Answer 1

Answer:

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:

73°,73°,107°,107°

Step-by-step explanation:

in parallelogram opposite angles are equal

3x-2=x+48

2x=50

x=25

thus angles is 73

now let the other two opposite angles be y

73+73+y+y = 360 ...sum of angles of a quadrilateral

2y = 214

y= 107

thus all angles are 73°,73°,107°,107°

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