Question

find the value of x. 5) 23° (3x + 1)° 6) (x + 9)° (6x + 5)°

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. In the first diagram, if we assume the two given angles are vertical angles, we set up the equation $23 = 3x+1$.

Step2: Solve the equation for $x$

Subtract 1 from both sides: $23 - 1=3x$, so $22 = 3x$. Then $x=\frac{22}{3}$.

Step3: For the second diagram

Assume the two given angles are corresponding angles (since the lines appear to be parallel - based on the context of angle - finding problems). We set up the equation $x + 9=6x+3$.

Step4: Rearrange the equation

Subtract $x$ from both sides: $9=6x - x+3$, so $9 = 5x+3$.

Step5: Solve for $x$

Subtract 3 from both sides: $9 - 3=5x$, so $6 = 5x$. Then $x=\frac{6}{5}$.

Answer:

For the first diagram: $x=\frac{22}{3}$; For the second diagram: $x=\frac{6}{5}$