Question

please help me I am in great trouble

Answer 1

41)
Answer.
Let ABCD be a parallalogram
Side AB = CD
Side AD = BC
Angles A and B form a linear pair
and angles C and D form a linear pair
Measure of angle A = C
and Measure of angle B = D
Angle A = C = 130
Angle B = D = 70

36)
Le the three consecutive odd numbers be: 
n + 1 
n + 3 and 
n + 5 
Therefore: 
n + 1 + n + 3 + n + 5 = 147 
Combine like terms: 
n + n + n = 3n 
1 + 3 + 5 = 9 
3n + 9 = 147 
Subtract 9 from each side of the equation. 
3n + 9 - 9 = 147 - 9 
9 - 9 = 0 
147 - 9 = 138 
3n = 138 
n = 46 
Therefore: 
n + 1 = 46 + 1 = 47 
n + 3 = 46 + 3 = 49 
n + 5 = 46 + 5 = 51 

Answer: 
The three consecutive odd numbers are: 
47, 49 and 51 

38)
If the interior angle of a regular polygon is 160 degrees, then the exterior angle is 20 degrees. The sum of all exterior angles is 360 degrees so there must be 360/20 sides = 18 sides.

39)
Each interior angle of the polygon is 108 degrees, so each exterior angle of the polygon is 180-108 = 72 degrees. So the number of sides is 360/72 = 5. Hence it is a regular pentagon. The sum of interior angles of a polygon with n sides is 180(n - 2).

Answer 2

36.- Let the three consecutive numbers whose sum is 147 be x+1 , x+3 , x+5 .
Therefore, x+1+x+3+x+5 = 147
3x+9 =147
3x=147-9
3x= 138
x=138/3
x= 46
Then,x+1= 46+1=47
x+3 =46+3= 49
x+5= 46+5= 51
Answer is 47, 49, 51