Question

the measures of the angle of a quadrilateral are in the ratio 1:2:3:4.find the measure of each angle l. what type of quadrilateral is it​

Answer 1

Answer:

Step-by-step explanation:

Given the four angles of a quadrilateral are in the ratio 1:2:3:4

Then Let the angles are x,2x,3x and 4x

We know that total of  four angles of a quadrilateral =360  

0

 

∴x+2x+3x+4x=360

⇒10x=360

⇒x=36  

0

 

hence the measures of  angles are 36⁰,72⁰,108⁰,144⁰  

Answer 2

Answer :-

• The measure of all angles of the quadrilateral is 36°, 72°, 108° and 144°.
• The type of quadrilateral is Parallelogram.

Step-by-step explanation :-

To Find,

• The measure of each angle of the quadrilateral
• What type of quadrilateral it is.

Solution,

Given that,

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

Let us assume given the ratio angles be 1x, 2x, 3x and 4x,

As we know that, the measure of a quadrilateral is 360°

➮ 1x + 2x + 3x + 4x = 360

➮ 10x = 360

➮ x = 360 / 10

➮ x = 36 ★

Hence, the value of x is 36.

The measure of the angles are,

• The measure of angle which we assumed as 1x

➮ 1x

➮ 1 × 36

➮ 36° ★

• The measure of angle which we assumed as 2x

➮ 2x

➮ 2 × 36

➮ 72° ★

• The measure of angle which we assume as 3x

➮ 3x

➮ 3 × 36

➮ 108° ★

• The measure of angle which we assume as 4x

➮ 4x

➮ 4 × 36

➮ 144° ★

Hence, the measure of all angles of the quadrilateral is 36°, 72°, 108° and 144°, the type of quadrilateral is a parallelogram.

Now, Verification

➮ 32 + 144 + 72 + 108 = 360°

➮ 180 + 180 = 360

➮ 360 = 360

L.H.S = R.H.S

Hence, Verified !