Question

1. given (mangle1=(12x - 24)^{circ}) and (mangle2=(6x + 42)^{circ}). solve for (x). 18. find (x). 7.g.5 ((x + 2)^{circ}) ((2x+19)^{circ}) 19. given (mangle1=(2x - 7)^{circ}) and (mangle2=(x + 49)^{circ}). solve for (x).

Explanation:

Step1: Set up equation for 17

Since vertical - angles are equal, we set \(12x - 24=6x + 42\).
\[12x-24 = 6x + 42\]

Step2: Isolate x - terms for 17

Subtract \(6x\) from both sides: \(12x-6x-24=6x - 6x+42\), which simplifies to \(6x-24 = 42\).
\[6x-24=42\]

Step3: Isolate the variable for 17

Add 24 to both sides: \(6x-24 + 24=42 + 24\), getting \(6x=66\). Then divide by 6: \(x = 11\).
\[x=\frac{66}{6}=11\]

Step4: Set up equation for 18

Since the sum of adjacent angles on a straight - line is \(180^{\circ}\), we have \((x + 2)+(2x+19)=180\).
\[x + 2+2x+19=180\]

Step5: Combine like - terms for 18

\(3x+21 = 180\).
\[3x+21=180\]

Step6: Isolate the variable for 18

Subtract 21 from both sides: \(3x+21-21=180 - 21\), getting \(3x = 159\). Then divide by 3: \(x = 53\).
\[x=\frac{159}{3}=53\]

Step7: Set up equation for 19

Since vertical - angles are equal, we set \(2x-7=x + 49\).
\[2x-7=x + 49\]

Step8: Isolate x - terms for 19

Subtract \(x\) from both sides: \(2x-x-7=x - x+49\), getting \(x-7 = 49\).
\[x-7=49\]

Step9: Isolate the variable for 19

Add 7 to both sides: \(x-7 + 7=49+7\), so \(x = 56\).
\[x=56\]

Answer:

1. \(x = 11\)
2. \(x = 53\)
3. \(x = 56\)