Question

Two adjacent angles of a parralelogram) (3y+10) (3y-4) Find all the angle

Answer 1

Answer :-

• Angles are 97°,83°,97° and 83° respectively.

Given :-

• Two adjacent angles of a parralelogram are (3y+10)° and (3y-4)°.

To Find :-

• All angles of the parallelogram.

Solution :-

Let ABCD be a parallelogram in which

• ∠A = (3y + 10)°
• ∠B = (3y - 4)°

As we know that

Adjacent angles of a parallelogram are supplementary.

According to question :-

⇒ (3y + 10) + (3y - 4) = 180

⇒ 3y + 10 + 3y - 4 = 180

⇒ 3y + 3y + 10 - 4 = 180

⇒ 6y + 6 = 180

⇒ 6y = 180 - 6

⇒ 6y = 174

⇒ y = 174/6

⇒ y = 29

• ∠A = 3y + 10 = 3(29) + 10 = 97°
• ∠B = 3y - 4 = 3(29) - 4 = 83°

Opposite angles of the parallelogram are equal

So,

• ∠A = ∠C = 97°
• ∠B = ∠D = 83°

Hence, all angles of the parallelogram are 97°,83°,97° and 83° respectively.

Answer 2

Question:

Two adjacent angles of a parralelogram (3y+10) (3y-4) Find all the angle.

Answer:-

• The angles of parallelogram are 97°, 83°, 97° and 83°

To find:-

• The angles of parallelogram

Solution:-

Let ABCD be a parallelogram .

• $\angle$A = 3y + 10
• $\angle$B = 3y - 4

• SUM OF ADJACENT ANGLES OF PARALLELOGRAM IS 180°

$\large{ : \implies (3y + 10) + (3y - 4) = 180}$

$\large{ : \implies \: 6y + 6 = 180}$

$\large{ : \implies \: 6y \: = 180 - 6}$

$\large{ : \implies \: 6y = 174}$

$\large{ : \implies \: y = \frac{174}{6} }$

$\large{ : \implies \: y = 29}$

OPPOSITE ANGLES OF PARALLELOGRAM ARE EQUAL

• $\angle \: A = \angle \: C$= 3y + 10 = 3×29 + 10 = 97°

• $\angle \: B = \angle \: D$= 3y - 4 = 3×29 - 4 = 83°

• The angles of parallelogram are 97°, 83°, 97° and 83°