Question

4. (i) The angles of a quadrilateral are in the ratio 1:2:3:4. Find all the anges.
(ii) The angles of a quadrilateral are in the ratio 2:5:7:10. Find the four anglies

please guys please help me​

Answer 1

180 degree

Step-by-step explanation:

sum of all interior angels of the quadrilateral = 360°

so the angles x,2x,3xand 4x

=x+2x +3x +4x =360°

=10x =360°

x=36

so here the angels will be x=36° 2x=72° 3x=108° 4x=144°

now we can see that

2x + 3x =72° + 108° = 180° and

x + 4x =36° + 144° = 180°

soo the adjacent pair of the agles are 180°

Answer 2

Answer:

(i) 36°, 72°, 108°, 144°

(ii) 30°, 75°, 105°, 150°

Step-by-step explanation:

(i) We know that the sum of all the angles of the quadrilateral is equal to 360°.

From the ratio of the angles of the quadrilaterals,

1x + 2x + 3x + 4x = 360° [ Here"x" represents the hightest

common factor (hcf) of all the

angles ]

Or, 10x = 360°

:. x = 36 °

Therefore, the angles are 36°, (36°×2) or 72°, (36°×3) or 108° and (36°×4) or 144°.

(ii) We know that the sum of all the angles of the quadrilateral is equal to 360°.

From the ratio of the angles of the quadrilaterals,

1x + 2x + 3x + 4x = 360° [ Here"x" represents the hightest

common factor (hcf) of all the

angles ]

Or, 10x = 360°

:. x = 36 °

Therefore, the angles are (15×2) or 30°, (15×5) or 75°, (15×7) or 105° and (15×10) or 150°.