the angles of quadrilateral are in A.P and the common difference is 10 degree. Find the angles?

Answer 1

Let the smallest angle of the quadrilateral is x degrees
Therefore the other 3 angles are x+10,X=20 and x+30
We know that the sum of intrior angles of a quadrilateral is 360 degrees
Hence,x+x+10+x+20+x+30=360
=>4x+60=360
=>4x=360-60=300
+.x=300/4=75
The angles are 75,85,95 and 105 degrees respectively

Answer 2

Sum of n terms in A.P.(Sn) = n/2 [2a+(n-1)d] .............(1)
WHERE
n= no. of terms
a= first term in A.P.
d= common difference

According to your question first take 4 angles like y , y+d , y+2d , y+3d & summation of 4 angles of a quadrilateral = 360 degree

here a = y , n = 4 , d = 10 & Sn = 360
Putting the value in equatoin (1) we have

Sn = n/2 [2a + (n-1) d ]

360 = 4/2 [ 2*y + ( 4-1) 10 ]

360 = 4y + 60

4y = 300

y = 300/4 = 75

so y = 75 degree
other 3 angles are y + d = 75+10 = 85degee

y + 2d = 75 + 20= 95degree

y + 3d = 75 + 30 = 105degree

So 4 angles are 75 , 85 , 95 , 105 degrees respectively .

Answer 3

Angles are a, a + d, a + 2d , a + 3d where a is first term and d is the common difference,10°

a + (a + 10) + (a + 20) + (a + 30) = 360
4a + 60 = 360
4a = 300
a = 75

Angles are 75°, 85°, 95° and 105°

Answer 4

let the angles be a-3d,a-d,a+3d,a+d.
a-d-a+3d=10 {common difference=10}
d=5
a-3d+a-d+a+3d+a+d=360 {sum of angles of quadrilateral}
a=90
so, a-3d= 90-3*5=75
a-d=90-5=85
a+3d=90+3*5=105
a+d=90+5=95
answer is 75,85,95,105

Answer 5

The sum of angles are always 360. So the answer could be...

360/4=90
90-20=70

The answer:
75, 85, 95, 105

COMO HAS GIVEN THE BEST ANSWER

Answer 6

75degree,85degree,95degree&105degree.