Question

Can someone please help Algerbra 1

Answer 1

`(5x-8)^(\circ)+(3x+12)^(\circ)=180^(\circ)`

x = 22

Explanation:

Linear Pair

Two adjacent angles that sum to 180° (two angles which when combined together form a straight line).

From inspection of the given diagram, line AB is a straight line.

Therefore, according to the linear pair theorem:

`\implies \angle ACD+\angle DCB=180^(\circ)`

`\implies (5x-8)^(\circ)+(3x+12)^(\circ)=180^(\circ)`

`\implies 5x-8+3x+12=180`

`\implies 5x+3x-8+12=180`

`\implies 8x+4=180`

`\implies 8x=176`

`\implies x=22`

Substitute the found value of x into each angle expression:

`\implies \angle ACD=(5(22)-8)^(\circ)`

`\implies \angle ACD=(110-8)^(\circ)`

`\implies \angle ACD=102^(\circ)`

`\implies \angle DCB=(3(22)+12)^(\circ)`

`\implies \angle DCB=(66+12)^(\circ)`

`\implies \angle DCB=78^(\circ)`

Answer 2

Equation: (5x - 8) + (3x + 12) = 180

x = 22

Explanation:

We can tell that ACB is a straight line and that a straight line is equal to 180 degrees. Using this logic, we will write our equation;

Given:

(5x - 8) + (3x + 12) = 180

Combine like terms:

8x + 4 = 180

Subtract 4 from both sides of the equation:

8x = 176

Divide both sides of the equation by 8:

x = 22