Question

the angles of a quadrilateral are in the ratio of 1 :2:3:4 find what is the measure of four angles​

Answer 1

Answer:

Now, it is very well known that the sum of all the interior angles of the quadrilateral is 360 degrees. So here the angles will be x=36∘, 2x=72∘, 3x=108∘, and 4x=144∘. So the adjacent pair of angles is 180 degrees.

Step-by-step explanation:

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Answer 2

Answer

The angles of quadrilateral are 36°, 72°, 108° and 144°.

Step-by-step explanation:

To Find :-

• The measure of four angles of quadrilateral.

★ Solution

Given that,

• The angles of quadrilateral are in the ratio of 1:2:3:4

Let us assume the given unknown angles as (1x), (2x), (3x) and (4x).

We know,

Sum of all angles of quadrilateral = 360°

∴ 1x + 2x + 3x + 4x = 360

Therefore,

⇒ 1x + 2x + 3x + 4x = 360

⇒ 3x + 3x + 4x = 360

⇒ 6x + 4x = 360

⇒ 10x = 360

⇒ x = 360/10

⇒ x = 36

The value of x is 36.

Now, The angles of quadrilateral are :-

• 1x = 1*36 = 36°
• 2x = 2*36 = 72°
• 3x = 3*36 = 108°
• 4x = 4*36 = 144°

Hence,

• The angles are 36°, 72°, 108° and 144°.

V E R I F I C A T I O N :-

• 1x + 2x + 3x + 4x = 360

By putting the value [1x,2x,3x,4x] in L.H.S and simplifying :-

⇒ 1x + 2x + 3x + 4x

⇒ 36 + 72 + 108 + 144

⇒ 180 + 180

⇒ 360

Now, L.H.S = R.H.S

Hence, Verified!