The exterior angles of a quadrilateral are in the ratio 1:4:4:6. What

Sum of exterior angles is 360
largest exterior angle = (6/15)*360 = 144
smallest exterior angle = (1/15)*360 = 24

largest interior angle = 180-24 = 156
smallest interior angle = 180-144 = 36

Their difference = 156-36 = 120

B is correct

Option B

We know that the sum of the angles of a quadrilateral = 360.

Let's call the smallest angle: \(x\)
The others will be \(4x, 4x , 6x\).

The smallest angle will be:
\(x+4x+4x+6x=360\)
\(x=24\)

The difference between the largest and the smallest will be:
\(6x-x=5x\)

Consequently,
\(5x=5*24=120\)

The exterior angles of a quadrilateral are in the ratio 1:4:4:6. What is the difference between the largest and the smallest interior angles of the quadrilateral?

(A) 140
(B) 120
(C) 110
(D) 100
(E) 60

Let the exterior angles be x, 4x, 4x & 6x
Formula: Sum of exterior angles of any n-sided polygon = 360 deg
--> x + 4x + 4x + 6x = 360
--> 15x = 360
--> x = 24 deg

Note: At any vertex, Interior angle + Ext. angle = 18
--> Interior angle is highest when exterior angle is lowest & vie versa

--> Highest interior angle = 180 - x & lowest interior angle = 180 - 6x
Difference = 180 - x - (180 - 6x) = 6x - x = 5x = 5*24 = 120 deg

Option B

sum of exterior angles = 360
sum of ratio sides; 15x = 360
x= 24
smallest side = 24
and largest = 144
∆ = 120
IMO B


The exterior angles of a quadrilateral are in the ratio 1:4:4:6. What is the difference between the largest and the smallest interior angles of the quadrilateral?

(A) 140
(B) 120
(C) 110
(D) 100
(E) 60

The exterior angles of a quadrilateral are in the ratio 1:4:4:6. What is the difference between the largest and the smallest interior angles of the quadrilateral?

(A) 140
(B) 120
(C) 110
(D) 100
(E) 60

Since each exterior angle of the quadrilateral would be a supplementary angle to each interior angle and sum of all interior angles is (n-2)*180 where n is number of sides, sum of exterior angles would be 360˚. ∠A, ∠B, ∠C and ∠D are interior angles.

Also, exterior angles are in ratio 1:4:4:6(∠A' : ∠B' : ∠C' : ∠D'). So let sum of all exterior angles = 15x

Let ABCD be the quadrilateral. So,
∠A + ∠B + ∠C + ∠D = 360˚
180˚ - ∠A' + 180˚ - ∠B' + 180˚ - ∠C' + 180˚ - ∠D' = 360˚ (∠A', ∠B', ∠C' and ∠D' are exterior angles supplementary to ∠A, ∠B, ∠C and ∠D respectively)
720˚ - (∠A' + ∠B' + ∠C' + ∠D') = 360˚
(∠A' + ∠B' + ∠C' + ∠D') = 360˚
15x = 360˚
x = 24˚
∠A' = 24˚ So ∠A = 156˚
∠B' = 4*24˚
∠C' = 4*24˚
∠D' = 6*24˚ ∠D = 36˚

∠A - ∠D = 156˚- 36˚ = 120˚

Answer B.

The ratio of the exterior angles are 1:4:4:6.
It is worth noting that the sum of the exterior and interior angles equals 180. Hence the corresponding interior angles will be in the ratio 6:4:4:1
The difference between the largest and smallest interior angles = (6-1)/15 * 360 = 5/15 * 360 = 120.

The answer is B.

The sum of the interior angles of a quadrilateral is 360.
--> (180-x)+ (180-4x)+ (180-4x)+ (180-6x)= 360
720 - 15x = 360
--> 15x=360
x= 24
--> the difference between the largest angle and the smallest angle:
(180-x) -(180-6x) = 5x --> 5*24= 120

The answer is B.

The exterior angles of a quadrilateral are in the ratio 1:4:4:6. What is the difference between the largest and the smallest interior angles of the quadrilateral?

(A) 140
(B) 120
(C) 110
(D) 100
(E) 60

Sum of the interior angle of of a quadrilateral is 180(n-2)
N is the side therefore for a four sided quadrilateral 180(4-2)=360
The smallest exterior angle will yield the largest Interior angle but anyways

1/15 (360) =24
6/15 (360) =144
144-24=120
Therefore, B

Posted from my mobile device

Ans: B

sum of exterior angles=360
so, x+4x+4x+6x=360
x=24
now, difference between the largest and the smallest interior angles of the quadrilateral= (180-24)-(180-(24*6))=120

The sum of exterior angles of a quadrilateral \(= 360°\)

.
Hence,

\(\\
-->x + 4x + 4x + 6x = 360\\
\\
-->15x = 360\\
.\\
-->x = 24\\
\)


So, smallest interior angle is
\(x = 24\\
\)
Largest interior angle is
\(6x = 6 * 24 = 144\\
\)

\(Difference = 144 - 24 = 120\\
\)
Option (B)

Posted from my mobile device

We know that the sum of all angles of a quadrilateral is 360. So we put x in the ratios 1x 4x 4x 6x .then we add the ratios 4+1+4+6= 15x then we divide it by 360 . x = 360/15= 24. 6x-1x=5x=5*24 =120 answer option b