Question

Which statement best completes the sentence below? If the measure of /_4 is 70^o, then the measure of /_8 is _________________. A 110^o because /_4 and /_8 are supplementary angles. B 70^o because /_4 and /_8 are alternate exterior angles. C 110^o because /_4 and /_8 are corresponding angles. D 70^o because /_4 and /_8 are corresponding angles.

Answer 1

Answer:

As given, measure of angle 4 is 70°

Then what would be the measure of ∠8.

Following cases comes into consideration  

1. If ∠4 and ∠8 are supplementary angles i.e lie on same side of Transversal, then

 ∠4 + ∠8=180°

⇒70°+∠8=180°  [∠4=70°]

⇒∠8=180°-70°

⇒∠8=110°

2nd possibility

But if these two angles i.e ∠4 and ∠8 forms a linear pair.Then

⇒ ∠4 + ∠8=180°

⇒70°+∠8=180°  [∠4=70°]

⇒∠8=180°-70°

⇒∠8=110°

3rd possibility

If ∠4 and ∠8 are alternate exterior angles.

then, ∠4 = ∠8=70°

4th possibility

If If ∠4 and ∠8 are corresponding angles.

then, ∠4 = ∠8=70°

Out of four options given Option A[ 110° because ∠4 and ∠8 are supplementary angles], Option B[70° because ∠4 and ∠8 are alternate exterior angles.] and Option D[70° because ∠4 and ∠8 are corresponding angles.] are Correct.