Question

In the figure below, c || d. Classify each of the following angle pairs, and tell whether they arecongruent or supplementary.6. 21 and 23Supp.7. 26 and 23Supp.8. 21 and 283/47/8Supp.5/6t9. 27 and 24Supp.10. 22 and 21& Supp.

Answer 1

Two angles are congruent if they are equal and supplementary if there sum is 180.

Given data:

c and d are parallel.

Now

`\angle1,\angle3`

are corresponding angles, so they are equal.

So,

`\angle1,\angle3`

form a congruent pair.

Now since

`\angle1=\angle6`

since they are vertically oppsoye angles.

And,

`\angle1=\angle3(\text{corresponding angles)}`

So,

`\angle6=\angle3`

So,

`\angle6,\angle3`

form a congruent pair.

Now,

`\begin{gathered} \angle3=\angle8(vertically\text{ opposite angles)} \\ \angle1=\angle3(corresponding\text{ angles)} \\ \Rightarrow\angle1=\angle8 \end{gathered}`

So,

`\angle1,\angle8`

form a congruent pair.

`\angle7=\angle4(vertically\text{ opposite angles)}`

So,

`\angle7,\angle4`

form a congruent pair.

Now,

`\angle1+\angle2=180(linear\text{ pair)}`

So,

`\angle1,\angle2`

form a supplementary pair.