Question

in a parallelogram, consecutive angles are
$(x - 5) and (2x + 5).$
find the measure of each angle.​

Answer 1

Answer :-

The angles of parallelogram are :-

• 55°
• 125°
• 55°
• 125°

Step-by-step explanation :

To Find :-

• The measure of each angles

Solution :-

Given that,

• In a Parallelogram, the consecutive ( adjacent ) angles are ( x - 5 )° and ( 2x + 5 )°

As we know that,

Adjacent angles of parallelogram = 180°,

Hence,

• ( x - 5 ) + ( 2x + 5 ) = 180°

=> x - 5 + 2x + 5 = 180

=> 3x - 5 + 5 = 180

=> 3x = 180

=> x = 180/3

=> x = 60

• The value of x is 60.

Now, the angles of parallelogram are:

• ( x - 5 )°

=> x - 5

=> 60 - 5

=> 55°

• ( 2x + 5 )°

=> 2x + 5

=> 2*60 + 5

=> 120 + 5

=> 125°

Therefore, the other two angles are :-

The angle opposite to ( x - 5 )° or 55° = 55° and the angle opposite to ( 2x + 5 )° or 125° = 125°, As opposite angles of parallelogram are equal.