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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.

In the figure below c d Classify each of the following angle pairs and tell whether they arecongruent or supplementary6 21 and 23Supp7 26 and 23Supp8 21 and 283 class=

Respuesta :

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

Given data:

c and d are parallel.

Now

[tex]\angle1,\angle3[/tex]

are corresponding angles, so they are equal.

So,

[tex]\angle1,\angle3[/tex]

form a congruent pair.

Now since

[tex]\angle1=\angle6[/tex]

since they are vertically oppsoye angles.

And,

[tex]\angle1=\angle3(\text{corresponding angles)}[/tex]

So,

[tex]\angle6=\angle3[/tex]

So,

[tex]\angle6,\angle3[/tex]

form a congruent pair.

Now,

[tex]\begin{gathered} \angle3=\angle8(vertically\text{ opposite angles)} \\ \angle1=\angle3(corresponding\text{ angles)} \\ \Rightarrow\angle1=\angle8 \end{gathered}[/tex]

So,

[tex]\angle1,\angle8[/tex]

form a congruent pair.

[tex]\angle7=\angle4(vertically\text{ opposite angles)}[/tex]

So,

[tex]\angle7,\angle4[/tex]

form a congruent pair.

Now,

[tex]\angle1+\angle2=180(linear\text{ pair)}[/tex]

So,

[tex]\angle1,\angle2[/tex]

form a supplementary pair.

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