Question

Two adjacent angles of a parallelogram are (3x-4) and (3×+16) then find the measurement of each angle ​

Answer 1

Answer:

Step-by-step explanation:

Given ,

The two adjacent angles are :- (3x-4)° and (3x + 16)°

We know that ,

Sum of adjacent angles in parallelogram are supplementary.

i.e sum of adjacent angles is 180°

=> (3x-4) + (3x+ 16) = 180°

=> 3x-4+3x+16 = 180°

=> 6x + 12 = 180°

=> 6x = 180-12

=> 6x = 168°

=> x = 168/6

=> x = 28

So , angles are

(3x - 4) = 3(28) - 4 = 80°

(3x + 16) = 3(28)+16 = 100°

We know,

Opposite angles in parallelogram are equal ,

So measure of each angle is 80°,100°,80°,100°

Answer 2

AnswEr :

• Adjacent Angle₁ = (3x - 4)°
• Adjacent Angle₂ = (3x + 16)°

The measures of the adjacent angles of a parallelogram add up to be 180°, or they are supplementary.

• So According to the Question Now :

⇒ Adj. Angle₁ + Adj. Angle₂ = 180°

⇒ (3x - 4) + (3x + 16) = 180°

⇒ 3x - 4 + 3x + 16 = 180

⇒ 6x + 12 = 180

⇒ 6x = 180 - 12

⇒ 6x = 168

• Dividing Both term by 6

⇒ x = 28

_________________________________

⇝ Angle₁ = (3x - 4) = 3(28) - 4 = 80°

⇝ Angle₂ = (3x + 16) = 3(28) + 16 = 100°

The Measures of Opposite Angles of Parallelogram are Equal. therefore,

◗ Angle₁ = Angle₃ = 80°

◗ Angle₂ = Angle₄ = 180°

∴ Angles are 80°,100°,80° and 100°.