Answer:
Arc DB = 146
x = 5
Step-by-step explanation:
Remark
The relationship between the large arc, the small arc and the intersecting angle is
1/2 (large arc - small arc) = intersecting angle.
Givens
Large arc = 25x + 21
Small arc = 96
5x
Solution
1/2*(25x + 21 - 96) = 5x*2 Multiply both sides by 2
25x + 21 - 96 = 10 x Combine
25x - 75 = 10x Subtract 25x from both sides
-75 = 10x - 25x
-15x = -75
x = 5
DB = 25x + 21
DB = 25*5 + 21
DB = 125 + 21
DB = 146
Tell me if this is not in the choices.
Supplementary angles are angles that add up to 180 degrees
Answer = 180 - 142 = 38 degrees
All the angles inside a quadrilateral add to 360 degrees.
But first, we should solve for x
Opposite angles add up to 180 degrees.
So we'll use angles B and D
x + 10 + x + 24 = 180
combine like terms
2x + 34 = 180
subtract 34 from both sides
2x = 146
divide both sides by 2
x = 73
Now let's solve for the angles
Angle D: x + 24 = 97
Angle B: x + 10 = 83
Angle A: x + 15 = 88
Opposite angles add up to 180
we know that angle A is 88
C + 88 = 180
subtract 88 from both sides
C = 92
Hope this helps!
