Question

the measure of an angle pf a parallelogram is 112° . find the measure of its remaining angle.​

Answer 1

Answer:

The angle opposite to the angle 112 is equal to it then the adjacent angle take as x now,x+112=180 then x is 58

Answer 2

The remaining angles of parallelogram are 112°, 68°, 68°

Given:

The measure of an angle of a parallelogram is 112°

To find:

Find the measure of its remaining angle

Solution:

Let A, B, C and D be the angles of a parallelogram such that the pair of angles ∠A, ∠C  and ∠B, ∠D are opposite angles

As we know Opposite angles in a parallelogram are equal

⇒ ∠A = ∠C and  ∠B = ∠D  

Given that an angle of parallelogram = 112

⇒ Take ∠A = ∠C = 112

Let ∠B = ∠D = x  

Sum of the angles in a Parallelogram = 360

⇒ ∠A + ∠C + ∠B + ∠D  

= 112° + 112°+ x° + x° = 360°

= 224°+2x° = 360°

= 2x° = 136°

= x = 68°

Therefore,

The remaining angles of parallelogram are 112°, 68°, 68°

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