Question

given the diagram, determine the relationship of each set of angles.
a) \\( \angle 1 \\) and \\( \angle 3 \\) are answer
b) \\( \angle 4 \\) and \\( \angle 6 \\) are answer
c) \\( \angle 6 \\) and \\( \angle 3 \\) are answer
d) \\( \angle 2 \\) and \\( \angle 6 \\) are answer
e) \\( \angle 2 \\) and \\( \angle 8 \\) are answer
f) \\( \angle 1 \\) and \\( \angle 8 \\) are answer

Explanation:

a) $\angle1$ and $\angle3$

• Step1: Analyze the position

$\angle1$ and $\angle3$ are adjacent and their non - common sides form a straight line.
So, $\angle1+\angle3 = 180^{\circ}$.

b) $\angle4$ and $\angle6$

• Step1: Analyze the position

$\angle4$ and $\angle6$ are on the inner side of the two lines \(n\) and \(r\) and on the opposite side of the transversal \(a\).

c) $\angle6$ and $\angle3$

• Step1: Analyze the position

$\angle6$ and $\angle3$ are on the inner side of the two lines \(n\) and \(r\) and on the same side of the transversal \(a\).

d) $\angle2$ and $\angle6$

• Step1: Analyze the position

$\angle2$ and $\angle6$ are on the outer side of the two lines \(n\) and \(r\) and on the same side of the transversal \(a\).

e) $\angle2$ and $\angle8$

• Step1: Analyze the position

$\angle2$ and $\angle8$ are on the outer side of the two lines \(n\) and \(r\) and on the opposite side of the transversal \(a\).

f) $\angle1$ and $\angle8$

• Step1: Analyze the position

First, $\angle1=\angle3$ (vertical angles). Then, $\angle3$ and $\angle8$ are on the inner side of the two lines \(n\) and \(r\) and on the opposite side of the transversal \(a\) (alternate interior angles).

Answer:

a) Supplementary angles
b) Alternate interior angles
c) Consecutive interior angles
d) Corresponding angles
e) Alternate exterior angles
f) Alternate exterior angles