Question

Plz, answer correctly

Answer 1

Given:

• PQ || RS
• EF || QS
• ∠PQS = 60°

To find:

• m∠RFE

Solution:

Here, we will use the property of a transversal cutting two parallel rays. We must remember that:

1) Corresponding angles are equal.

2) Alternate interior angles are equal.

3) Alternate exterior angles are supplementary.

4) Interior angles on the same side of the transversal are supplementary.

We know the measure of ∠PQS. From ∠PQS, we can find the measure of ∠QSF as they are a pair of interior angles on the same side of the transversal, QS. From rule 4),

∠PQS + ∠QSF = 180°

60° + ∠QSF = 180°

∠QSF = 180° - 60°

∠QSF = 120°

Now, we can easily find the measure of ∠RFE, as we found the measure of ∠QSF. How? ∠RFE and ∠QSF are corresponding angles. Recalling from the very first rule, corresponding angles are equal.

So,  m∠RFE = m∠QSF

      m∠RFE = 120°

Therefore, the measure of ∠RFE is 120°.