Question

measure of angle of quadrilateral ABCD are in ratio of 1:2:3:4 . show that quadrilateral ABCD is trapezium ​

Answer 1

Given :

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

To find :

• Angles if quadrilateral ABCD &
• Show that ABCD is a trapezium

According to the question,

Let,

• The ratio be 1x, 2x, 3x and 4x.

We know,

• Sum of all angles of quadrilateral = 360°

➞ 1x + 2x + 3x + 4x = 360°

➞ 3x + 7x = 360°

➞ 10x = 360°

➞ x = 360° ÷ 10

➞ x = 36°

★ Value of 1x :

➞ 1x

➞ 1(36°)

➞ 36° ....... ∠A)

★ Value of 2x :

➞ 2(36°)

➞ 72° ....... ∠B)

★ Value of 3x :

➞ 3x

➞ 3(36°)

➞ 108° ...... ∠C)

★ Value of 4x :

➞ 4x

➞ 4(36°)

➞ 144° ...... ∠D)

• So, the angles are 36°, 72°, 108° and 114°.

Now,

We have to prove that ABCD is a trapezium

➞ ∠A + ∠D = 180°

➞ 36° + 144° = 180°

➞ 180° = 180°

➞ ∠B + ∠C = 180°

➞ 72° + 108° = 180°

➞ 180° = 180°

So, we can say that ABCD is a trapezium.

Answer 2

Answer:

Given

Angles of an quadrilateral ABCD are in the ratio given : 1:2:3:4

To find out

1. Angles of quadrilateral ABCD
2. Also, show ABCD is an trapezium

Step-by-step explanation:

Let

• The ratio given be let as x

Let the ratio be 1x,2x,3x,4x (derived from : 1:2:3:4)

Knowledge required to solve

• Sum of all the angles of a quadrilateral is 360 °

1. Now let's solve it step - by - step

=》 1x+2x+3x+4x = 360°

=》 3x+3x+4x=360°

=》 6x +4x = 360 °

=》10x = 360 °

$= > x = \frac{360}{10}$

=》x= 36 °

Now one by one we have to find the X which it derived from ratio 1:2:3:4

$\blue{ \bigstar}value \: of \: 1x \:$

=》 1 ×36°

=》36 °_______ \_ A

$\pink{ \bigstar}value \: of \: 2x$

=》2×36°

=》72° _________ \_ B

$\green{ \bigstar}value \: of \: 3x$

=》3×36°

=》108 ° __________ \_ C

$\orange{ \bigstar}value \: of \: 4x \:$

=》4×36°

=》144°________ \_ D

•°• Therefore we got the four angles they are 36°,72°,108°,144°

2. We have now to prove that ABCD is a trapezium

\_ A + \_ D = 180 °

=》36°+144°= 180°

=》180 ° = 180 °

${ \frak{ \underline \purple{hence \: proved}}}$

\_ B +\_ C = 180 °

=》72 ° + 108 ° = 180 °

=》180 ° = 180°

${ \frak{ \underline \purple{hence \: proved}}}$

•°• Therefore we can say yes ABCD is a trapezium