please solve this question it is tuff for me
Answers
Answer:
A decagon has 10 sides
so these sides to be added! and should give a sum of 1440°
3x+10 + 2x+7 + 4x-3 + 5x-2 + 2x+15 + 3x+2 + x+3 + 2x+5 + 3x-1 + 3x+4 = 1440
( 3x + 2x + 4x + 5x + 2x + 3x + x + 2x + 3x + 3x ) + ( 10 + 7 - 3 - 2 + 15 + 2 + 3 + 5 - 1 + 4) = 1440
28x + 40 = 1440
28x = 1440 - 40
28x = 1400
x = 1400/28
x = 50
So the angles are =
(3*50 + 10) = 1st angle
160° = 1st angle
(2*50 + 7) = 2nd angle
107° = 2nd angle
(4*50 - 3) = 3rd angle
197° = 3rd angle
(5*50 - 2) = 4th angle
248° = 4th angle
(2*50 + 15) = 5th angle
115° = 5th angle
(3*50 + 2) = 6th angle
152° = 6th angle
(50 + 3) = 7th angle
53° = 7th angle
(2*50 + 5) = 8th angle
105° = 8th angle
(3*50 - 1) = 9th angle
149° = 9th angle
(3*50 + 4) = 10th angle
154° = 10th angle
Thus angles are given
hope it helps!
PLS MARK AS BRAINLIEST
Answer:
First we find the sum of interior angles of decagon:
Number of sides = 10
Formula = (n-2)180 where ‘n’ is the number of sides
⇒ (10-2)180
8×180
1440°
⇒ Angles of the decagon are:
(3x+10)°, (2x+7)°, (4x-3)°, (5x-2)°, (2x+15)°, (3x+2)°, (x+3)°, (2x+5)°, (3x-1)°, (3x+4)°
Sum of these angles:
28x + 40
⇒ 28x + 40 = 1440
28x = 1440 - 40
28x = 1400
x = 1400/28
x = 50
Now, we substitute the value of ‘x’ in each angle:
(3x+10)°
= 3(50)+10
= 150 + 10
= 160°
(2x+7)°
= 2(50)+7
= 100 + 7
= 107°
(4x-3)°
= 4(50)-3
= 200 - 3
= 197°
(5x-2)°
= 5(50)-2
= 250 - 2
= 248°
(2x+15)°
= 2(50)+15
= 100 + 15
= 115°
(3x+2)°
= 3(50)+2
= 150 + 2
= 152°
(x+3)°
= 50 + 3
= 53°
(2x+5)°
= 2(50)+5
= 100 + 5
= 105°
(3x-1)°
= 3(50)-1
= 150 - 1
= 149°
(3x+4)°
= 3(50)+4
= 150 + 4
= 154°
VERIFY:
We have to see whether the sum of all our angles is equal to 1440°
⇒ 160+107+197+248+115+152+53+105+149+154 = 1440
1440 = 1440
LHS = RHS
Hence, verified
Hope it helps
Please mark my answer as BRAINLIEST