Question

the sum of two opposite angles of a parallelogram is120 find all the angles​

Answer 1

Answer:

Hii !! Thanks A2A :)

In any parallelogram, opposite sides are parallel (which is the definition of parallelogram :) )

Due to this opposite angles are equal.

As in the above diagram, in any parallelogram ABCD, ∠A = ∠C = let ‘x’

and ∠B = ∠D = let ‘y’

Now according to the question, ∠A + ∠C = 120° or you can also take ∠B + ∠D = 120° (since opposite angles)

So, ∠x + ∠x = 120°

=> 2∠x = 120°

=> ∠x = 60°

Since ∠x + ∠y = 180° (Angles between llel sides)

So, ∠y = 180° - ∠x

=> ∠y = 180° - 60°

=> ∠y = 120°

Therefore,

∠A = ∠x = 60°

∠B = ∠y = 120°

∠C = ∠x = 60°

∠D = ∠y = 120°

Step-by-step explanation:

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Answer 2

Answer:

Given:

• Sum of two opposite angles of a parallelogram is 120

Find:

• Find All angles?

Solution:

From Question, we understood that sum of opposite angles are equal

${ \sf{ \to{x + x = 120}}} \\ \\ { \sf{ \to{2x = 120}}} \\ \\ { \sf{ \to{x = \frac{120}{2} }}} \\ \\ { \sf{ \to{x = 60}}}$

So, ∠ A = 60° & ∠c = 60°

We already Know that :

${ \sf{ \to{x + y = 180 }}} \\ \\ { \sf{ \to{60 + y = 180}}} \\ \\{ \sf{ \to{y = 180 - 60}}} \\ \\ { \sf { \to{y = 120}}}$

So, ∠B = 120 , ∠D = 120

Therefore,

• ∠A = 60°
• ∠B = 120°
• ∠C = 60°
• ∠D = 120°