Question

8. Two opposite angles of a parallelogram
are (3x + 4)º and (5x – 2)°. Find
the measure of all the angles of the
parallelogram.​

Answer 1

Answer:

Step-by-step explanation:

Let,

1st Angle = 3x+4°

3rd Angle = 5x -2°

Opp. Angles OF A Parallelogram Are Equal,

3x+4 = 5x-2

3x - 5x = -2-4

-2x = -6

x = 3.

1st Angle : 3x + 4 = 3(3) + 4 = 9+4 = 13.

3rd Angle : 5(3) -2 = 15 -2 = 13.

Sum Of Adjacent Angles Of A Parallelogram Are Equal,

2nd Angle + 13 = 180

2nd Angle = 180-13 = 167°

Opp. Angles OF A Parallelogram Are Equal,

2nd Angle = 4th Angle

Therefore, 4th Angle = 167°

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Answer 2

Answer:

Let the other two angles be 'x'

As we know, sum of all angles of a parallelogram = 360°

So, LA+LB+LC+LD= 360°

3x+4+5x-2+x+x=360°

10x+2=360

10x=360-2

10x=358

x=358/10

x=35.8°

LA= 3x+4=3×35.8+4=11.4°

LB= 5x-2=5×35.8-2=177

LC=x=35.8°

LD=x=35.8°

Hence all the angles of a parallelogram = 11.4°, 177°, 35.8° and 35.8°