Question

.
2. If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram
3. The shorter side of a parallelogram is 3.6 cm and the longer side is half
side. Find the perimeter of the parallelogram.
4. One angle of the parallelograप्लीज आंसर एस फास्ट एस पॉसिबल ​

Answer 1

Step-by-step explanation:

Let x and y be two adjacent angles of a parallelogram.

According to the question,

⇒ x=

3

2

y ----- ( 1 )

We know in parallelogram, sum of adjacent angles are supplementary.

∴ x+y=180

o

.

⇒

3

2

y+y=180

o

[ From ( 1 ) ]

⇒ 2y+3y=540

o

⇒ 5y=540

o

⇒ y=108

o

.

Substituting value of y in equation ( 1 ) we get,

⇒ x=

3

2

×108

o

⇒ x=72

o

We know that, in parallelogram opposite angles are equal.

∴ Four angles of parallelogram are 108

o

,72

o

,108

o

and 72

o

.

Answer 2

Question 1:-

If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram.

━━━━━━━━━━━━━━━

Soluton:-

Let:-

• One angle be x
• The other be y

We know,

The sum of adjacent angles of a parallelogram = 180°

Thus,

• x + y = 180 ---- 1

Also given,

One of the angles is two third if it's adjacent angle.

Thus,

• x = (2/3)y----- 2

Substituting the value of x from equation 2 in equation 1 we get,

$\dfrac{2}{3}y + y = 180$

$\dfrac{2y + 3y}{3} = 180$

$5y =5 40$

$y = 108\degree$

Then x = 180 - 108

→ x = 72°

Thus the two angles are $\red{\boxed{\bold{\large{108 \degree \: and\: 72\degree}}}}$

━━━━━━━━━━━━━━━

Question 2:-

The shorter side of a parallelogram is 3.6 cm and the longer side is half and as much as the shorter side. Find the perimeter of the parallelogram.

━━━━━━━━━━━━━━━

Soluton:-

One side = 3.6 cm

Longer side = shorter side + (shorter side ÷2)

→ Longer side = 3.6 + (3.6÷2) cm

→ Longer side = 3.6 + 1.8 cm

→ Longer side = 5.4 cm

The perimeter = 2× shorter side + 2× longer side

→ Perimeter = 2 × (3.6 + 5.4)

→Perimeter = 2 × 9 cm

→ $\red{\large{\boxed {\bold{Perimeter = 18cm}}}}$