Question

if to adjacent angle of a parallelogram are (5x-5)° and (10x +35 )° then find the angel of these angles
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Answer 1

• The two adjacent angles of the parallelogram are 45° and 135°

Given:

Two adjacent angles of a parallelogram are (5x - 5)° and (10x + 35)°

To find:

The value of these two angles.

Now,

Some properties of a parallelogram,

• The opposite sides are parallel.
• The opposite sides are equal.
• The sum of the adjacent angles of a parallelogram is 180°. [As they become two interior angles between two parallel with one transversal line]

So,

⇒ (5x - 5)° + (10x + 35)° = 180°

⇒ 5x - 5 + 10x + 35 = 180

⇒ 15x + 30 = 180

⇒ 15x = 180 - 30

[By taking 30 to RHS]

⇒ 15x = 150

⇒ x = 150 ÷ 15

[By taking 15 to RHS]

⇒ x = 10

Thus,

The value of x is 10

Now,

The value of two angles

⇒ (5x - 5)°

= 5 * 10 - 5

= 50 - 5

= 45°

And,

⇒ (10x + 35)°

= 10 * 10 + 35

= 100 + 35

= 135°