Question

In the parallelogram ABCD angle A is 55 . Find all the other angles

Answer 1

Answer:

opposite angles of a parallelogram are congruent

angle A=angle C

angle B=angle D

angleC=55

angleA+B+C+D=360

therefore,

55+B+55+D=360

110+B+D=360

sinceB=D,

110+B+B=360

110+2B=360

2B=360-110

2B=250

B=250÷2

B=125

therefore,

D=125

hence,

C=55

B=125

D=125

Answer 2

Answer:

The other angles are 125°, 55° and 125°.

Step-by-step explanation:

Given:-

ABCD is a parallelogram such that ∠A = 55°.

To find:-

All the other angles, i.e., ∠B, ∠C and ∠D.

Step 1 of 2

As we know,

The sum of $2$ adjacent angles of a parallelogram is $180$°.

Since it is given that ABCD is parallelogram and ∠A = 55°.

So,

∠A + ∠B = 180° (A and B are adjacent angles)

55° + ∠B = 180°

         ∠B = 180° - 55°

         ∠B = 125°

Step 2 of 2

In a parallelogram, the measure of the opposite angles are equal.

Since ∠A and ∠C, ∠B and ∠D are opposite angles.

Thus,

∠C = ∠A

∠C = 55°

And,

∠D = ∠B

∠D = 125°

Therefore, the other angles are 125°, 55° and 125°.

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