Question

write answer for brainliest

Answer 1

Answer:

75°, 105°, 75°, 105°

Step-by-step explanation:

Given that ABCD is a parallelogram having angle A (2x + 27)° and angle C (3x + 3)°. We need to find out all the angles of a parallelogram.

Now, we now that opposite sides of a parallelogram are equal. So, we can say that angle A is equal to angle C.

→ (2x + 27)° = (3x + 3)°

→ 2x -3x = 3° - 27°

→ - x = - 24°

→ x = 24°

Therefore, angle A = (2x + 27)° = 2(24°) + 27° = 48° + 27° = 75° and angle C = (3x + 3)° = 3(24°) + 3° = 72° + 3° = 75°

(This too, can prove that opposite sides of a parallelogram are equal or you can prove by ASA criterion of concurrency triangle.)

Now,

Adjacent angles of a parallelogram are supplementary means their sum is 180°.

→ ∠A + ∠B = 180°

→ 75° + ∠B = 180° (angle A = 75° proved above)

→ ∠B = 180° - 75°

→ ∠B = 105° (similarly, ∠D = 105°)

Hence, the angles of the parallelogram are 75°, 105°, 75° and 105°.

Answer 2

$\bold\red{Answer}$

75°, 105°, 75°, 105°

Step-by-step explanation:

Given that ABCD is a parallelogram having angle A (2x + 27)° and angle C (3x + 3)°. We need to find out all the angles of a parallelogram.

Now, we now that opposite sides of a parallelogram are equal. So, we can say that angle A is equal to angle C.

→ (2x + 27)° = (3x + 3)°

→ 2x -3x = 3° - 27°

→ - x = - 24°

→ x = 24°

Therefore, angle A = (2x + 27)° = 2(24°) + 27° = 48° + 27° = 75° and angle C = (3x + 3)° = 3(24°) + 3° = 72° + 3° = 75°

(This too, can prove that opposite sides of a parallelogram are equal or you can prove by ASA criterion of concurrency triangle.)

Now,

Adjacent angles of a parallelogram are supplementary means their sum is 180°.

→ ∠A + ∠B = 180°

→ 75° + ∠B = 180° (angle A = 75° proved above)

→ ∠B = 180° - 75°

→ ∠B = 105° (similarly, ∠D = 105°)

Hence, the angles of the parallelogram are 75°, 105°, 75° and 105°.