Question

1. (3x + 20)° (x + 10)° type: x = - 5 7) x + 34° 2x - 12° type: x = 10) 3x + 21° x + 57° type: x = 11) x + 64° 3x - 26° type: x =

Explanation:

Step1: Identify vertical - angle relationship for problem 7

Vertical angles are equal. So, $2x - 12=x + 34$.

Step2: Solve the equation for $x$

Subtract $x$ from both sides: $2x-x-12=x - x+34$, which simplifies to $x-12 = 34$. Then add 12 to both sides: $x=34 + 12$.

Step3: Identify vertical - angle relationship for problem 10

Vertical angles are equal. So, $3x+21=x + 57$.

Step4: Solve the equation for $x$

Subtract $x$ from both sides: $3x - x+21=x - x+57$, which simplifies to $2x+21 = 57$. Then subtract 21 from both sides: $2x=57 - 21=36$. Divide both sides by 2: $x = 18$.

Step5: Identify corresponding - angle relationship for problem 11

Corresponding angles are equal. So, $x + 64=3x-26$.

Step6: Solve the equation for $x$

Subtract $x$ from both sides: $x - x+64=3x - x-26$, which simplifies to $64=2x-26$. Add 26 to both sides: $64 + 26=2x$, so $90=2x$. Divide both sides by 2: $x = 45$.

Answer:

1. Type: Vertical angles, $x = 46$
2. Type: Vertical angles, $x = 18$
3. Type: Corresponding angles, $x = 45$