M ABD = 10x - 7 and m2DBC = 3x + 5. What is the numerical value of m_ABD?
D
1
B

 71/7

Step-by-step explanation:

No picture is provided so I am assuming that BD is an angle bisector.

1. ∠ABD=10x-7, ∠DBC=3x+5           Given

2. ∠ABD = ∠DBC                             Definition of angle bisector

3. 10x-7 = 3x+5                                Substitution

4. 7x - 7 = 5                                      Subtraction Property of Equality

5. 7x = 12                                          Addition Property of Equality

6. x = 12/7                                         Division Property of Equality

7. ∠ABD = 10(12/7) - 7                      Substitution

8. ∠ABD = 71/7                                 Adding like terms

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

hkhkhkhkhkhkhk

step-by-step explanation: