Question

solve for x:
name the relationship for each pair of angles below:
∠3 and ∠5
∠1 and ∠7
∠3 and ∠7
∠3 and ∠6

Explanation:

Step1: Identify vertical - angle property

Vertical angles are equal. The angles \(2x + 2^{\circ}\) and \(3x+8^{\circ}\) are vertical angles. So, we set up the equation \(2x + 2=3x + 8\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(2x+2-2x=3x + 8-2x\), which simplifies to \(2=x + 8\). Then subtract 8 from both sides: \(2-8=x+8 - 8\), so \(x=-6\).

Answer:

\(x=-6\)

For the angle - relationship part:

• If two lines are intersected by a transversal:
• \(\angle3\) and \(\angle5\) are same - side interior angles. They are on the same side of the transversal and between the two intersected lines.
• \(\angle1\) and \(\angle7\) are alternate exterior angles. They are on opposite sides of the transversal and outside the two intersected lines.
• \(\angle3\) and \(\angle7\) are corresponding angles. They are in the same relative position with respect to the transversal and the intersected lines.
• \(\angle3\) and \(\angle6\) are alternate interior angles. They are on opposite sides of the transversal and between the two intersected lines.