Answer:
B.
NB = 31
DN = 17
DB = 17
C.
∠N = 55°
∠B = 55°
∠D = 70°
Explanation:
B.
Isosceles triangles have 2 equal sides.
Given
DN = DB
** B is not shown on the image, it is to the right-most corner
Now, we equate the expressions for DN and DB and solve for x first:
DN = DB
4x + 1 = 6x - 7
1 + 7 = 6x - 4x
8 = 2x
x = 8/2
x = 4
Given,
NB = 5x + 11
DN = 4x + 1
DB = 6x - 7
Putting the value of x, we find length of each side.
NB = 5(4) + 11 = 31
DN = 4(4) + 1 = 17
DB = 6(4) - 7 = 17
So,
NB = 31
DN = 17
DB = 17
C.
Since DB = DN, the opposite angles are equal as well. So ∠N and ∠B are equal. Lets equate the expressions and find x first:
∠N = ∠B
x + 20 = 90 - x
2x = 90 - 20
2x = 70
x = 70/2
x = 35
So,
∠N = x + 20 = 35 + 20 = 55°
∠B = 90 - x = 90 - 35 = 55°
We know 3 angles in a triangle sum to 180. So we can find ∠D:
∠N + ∠B + ∠D = 180
55 + 55 + ∠D = 180
110 + ∠D = 180
∠D = 180 - 110
∠D = 70°
So,
∠N = 55°
∠B = 55°
∠D = 70°