Question

1) the measure of opposite side of a parallelogram are 7x + 20 cm and 8x - 30 cm find the length of the sides. 2) one of the diagonal of a rhombus is equals to one of its sides find the angles of the Rhombus

Answer 1

Question 1) :- the measure of opposite side of a parallelogram are 7x + 20 cm and 8x - 30 cm find the length of the sides ?

Solution :-

we know that , Opposite sides of a parallelogram are equal to each other.

So,

→ 7x + 20 = 8x - 30

→ 8x - 7x = 20 + 30

→ x = 50cm.

Therefore,

→ Length of 2 given sides will be = 7x + 20 = 7*50 + 20 = 350 + 20 = 370 cm. (Ans.)

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Question 2) :- one of the diagonal of a rhombus is equals to one of its sides find the angles of the Rhombus ?

Solution :-

we know that, all the sides of a rhombus are equal in length .

So,

we can conclude that, when diagonal of a rhombus is equal to one of its sides , than it will be equal to all sides.

Than,

Triangle made my 2 adjacent sides of rhombus and diagonal have all sides are equal. Therefore, it a Equaliteral Triangle.

• Each angle of an Equaliteral Triangle is equal to 60° .

Therefore,

→ Angle between to adjacent sides of rhombus also = 60° .

Now, we also know that, Opposite angles of a rhombus have equal .

Hence, Opposite angle is also equal to 60°.

Let rest to angles are x° each.

Than,

→ x + x + 60° + 60° = 360° . (Angle sum Property).

→ 2x + 120° = 360°

→ 2x = 360° - 120°

→ 2x = 240°

→ x = 120° .

∴ all angles of given rhombus are (60°, 120°, 60°, 120°.)