Question

Adjecent angles of parallelogram are(3x-150)degree and (2x+50)degree. Find all angles of the parallelogram.​

Answer 1

Answer:

3x-150+2x+50=180, degree (co interior angles)

=>5x - 100 = 180

=>5x = 180 + 100

=>5x = 280

=>x = 280/5 = 56

angles are 18 degree and 150

Answer 2

Given:-

• Adjacent angles of the parallelogram = (3x - 150)° and (2x + 50)°

To Find:-

• All the angles of the parallelogram

Note:-

• Refer to the attachment for the figure.

Solution:-

Let us recall the theorem which says:-

• The anjacent angles of a parallelogram are always supplementary.

Hence,

∠DAB + ∠ABC = 180°

= (3x - 150)° + (2x + 50)° = 180°

⇒ 3x - 150 + 2x + 50 = 180°

⇒ 5x - 100° = 180°

⇒ 5x = 180° + 100°

⇒ 5x = 280°

⇒ x = 280/5

⇒ x = 56°

Putting respective values:-

∠DAB = 3x - 150°

⇒ ∠DAB = 3 × 56° - 150°

⇒ ∠DAB = 168° - 150°

⇒ ∠DAB = 18°

Also,

∠ ABC = 2x + 50°

⇒ ∠ABC = 2 × 56° + 50°

⇒ ∠ABC = 112° + 50°

⇒ ∠ABC = 162°

∴∠DAB = 18° and ∠ABC = 162°

For other angles:-

• ∠ADC = ∠ABC = 162° [Vertically Opposite ∠s]
• ∠DCB = ∠DAB = 18° [Vertically Opposite ∠s]

Hence, All the angles of the Parallelogram are as follows:-

• ∠DAB = 18°
• ∠ABC = 162°
• ∠DCB = 18°
• ∠ADC = 162°

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Extra Informations:-

• A parallelogram is a quadrilateral with its opposite sides parallel.

• The opposite angle of the parallelogram is always equal.

• The adjacent angles of the parallelogram is always supplementary.

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