Question

a) name the relation between the angles formed by the transversal in the figure below.
∠1 and ∠8 =
∠4 and ∠6 =
∠4 and ∠5 =
∠2 and ∠6 =
∠3 and ∠5 =
∠3 and ∠6 =
∠1 and ∠5 =
∠2 and ∠7 =

Explanation:

• For \(\angle1\) and \(\angle8\): Alternate exterior angles are non - adjacent angles that lie outside the two lines and on opposite sides of the transversal. \(\angle1\) and \(\angle8\) fit this definition.
• For \(\angle4\) and \(\angle6\): Alternate interior angles are non - adjacent angles that lie between the two lines and on opposite sides of the transversal. \(\angle4\) and \(\angle6\) meet this criterion.
• For \(\angle4\) and \(\angle5\): Consecutive interior angles (also known as same - side interior angles) are angles that lie between the two lines and on the same side of the transversal. \(\angle4\) and \(\angle5\) satisfy this.
• For \(\angle2\) and \(\angle6\): Corresponding angles are in the same relative position (e.g., both above the lines and on the same side of the transversal). \(\angle2\) and \(\angle6\) are in corresponding positions.
• For \(\angle3\) and \(\angle5\): Alternate interior angles (non - adjacent, between the lines, opposite sides of transversal). \(\angle3\) and \(\angle5\) follow this rule.
• For \(\angle3\) and \(\angle6\): Consecutive interior angles (between the lines, same side of transversal). \(\angle3\) and \(\angle6\) are consecutive interior.
• For \(\angle1\) and \(\angle5\): Corresponding angles (same relative position). \(\angle1\) and \(\angle5\) are in corresponding positions.
• For \(\angle2\) and \(\angle7\): Alternate exterior angles (non - adjacent, outside the lines, opposite sides of transversal). \(\angle2\) and \(\angle7\) fit the alternate exterior angle definition.

Answer:

• \(\angle1\) and \(\angle8\): Alternate exterior angles
• \(\angle4\) and \(\angle6\): Alternate interior angles
• \(\angle4\) and \(\angle5\): Consecutive interior angles
• \(\angle2\) and \(\angle6\): Corresponding angles
• \(\angle3\) and \(\angle5\): Alternate interior angles
• \(\angle3\) and \(\angle6\): Consecutive interior angles
• \(\angle1\) and \(\angle5\): Corresponding angles
• \(\angle2\) and \(\angle7\): Alternate exterior angles