Question

Hey guys,



please help me with this 3 questions of mathematics


1. Find angle which is equal to its complement??


2. Find the angle which is equal to its supplement????




3. In the given figure, angle 1 and angle 2 are supplementary angles.


if angle 1 is decreased what changes should take place in angle 2 so that the angles still remain supplementary..( angle pic is above)



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please answer fast...

Answer 1

Step-by-step explanation:

(1)

Let the angle be 'x'.

Given that the angle is equal to its complement.

So, complement angle = x.

Now,

We know that Two angles are complementary when they add upto 90°.

⇒ x + x = 90°

⇒ 2x = 90°

⇒ x = 45°.

(2)

Let the angle be 'x'.

Then, the supplementary be 'x'.

If two angles are supplementary,their sum is 180°.

⇒ x + x = 180°

⇒ 2x = 180°

⇒ x = 90°.

(3)

From figure, we can say that ∠1 and ∠2 supplementary angles.

If ∠1 is reduced, ∠2 should be increased by the same measure so that the angles still remain supplementary.

Hope it helps!

Answer 2

Answer:

1.

45°

2.

90°

3.

angle 2 will increase by same value as angle 1 decreased

Step-by-step explanation:

1)

complements of an angle means the angles which sum out to 90

acc. to the given condition we can consider equal angles a and a (as they are equal) and work accordingly;

a+a=90

a=90/2

a=45°

2)

same is the case with supplementary the difference is that the sum of angles is 180

so;

a+a=180

a=180/2

a=90°

3)

now as we have already seen the meaning of the term supplementary;

we can further proceed logically by thinking that;

the sum of the new changed angles should also be 180°

so, as angle 1 is decreased by say x°, to maintain the sum as 180°, angle 2 should also increase by x°.

thus they will remain supplementary.