Question

Geometry. Attached photo. PLEASE FOR THE LOVE OF GOD.

Answer 1

Explanation:

`\angle{DBC }`=(5x+4)°

`\angle{ A }`=(2x-2)°

`\angle{C }`=(4x-6)°

we know that,

`\angle{DBC}`=
`\angle{A}`+
`\angle{C}`

According to the question,

`\tt{ 5x+4=2x-2+4x-6 }`

`\tt{ 5x+4=6x-8 }`

`\tt{ 6x-5x=4+8 }`

`\bold{x=12 }`

so,

`\angle{C }`=(4x-6)°=(4×12-6)°=(48-6)°=42°

Answer 2

m<C = 42°

Explanation:

Given:

m<A = (2x - 2)°

m<C = (4x - 6)°

m<DBC = (5x + 4)°

Thus:

m<DBC = m<A + m<C (exterior angle theorem of a triangle)

(5x + 4)° = (2x - 2)° + (4x - 6)°

Solve for x

5x + 4 = 2x - 2 + 4x - 6

Collect like terms

5x + 4 = 6x - 8

5x - 6x = -4 - 8

-x = -12

Divide both sides by -1

x = 12

✔️m<C = (4x - 6)°

Plug in the value of x

m<C = 4(12) - 6 = 48 - 6

m<C = 42°