Question

Three parallel lines are intersected by a transversal. twelve angles are created. one of the angles measures 48° how many of the other angles have a measure of 48°?

Answer 1

Answer:

There are 5 more angles have a measure of 48°.

Step-by-step explanation:

Consider the provided information.

It is given that Three parallel lines are intersected by a transversal and twelve angles are created.

For better understanding you can refer the figure 1.

The figure 1 shows three parallel lines intersected by a transversal and have 12 angles.

It is given that one of the angles measures 48°

Pick any angle and suppose that the measure of angle is 48°.

Let say m∠1 = 48°

Thus, m∠1 = m∠5 = m∠9 = 48° (Corresponding angles are equal.)

Also, m∠1 = m∠3 (Vertical angles are always congruent or equal)

Similarly,

m∠5 = m∠7 and m∠9 = m∠11 (Vertical angles are always congruent)

Thus, the equal angles are:

m∠1 = m∠3= m∠5 = m∠7 = m∠9 = m∠11 = 48°

Therefore, the measure of 6 angles are equal when three parallel lines are intersected by a transversal.

Because you have already chosen one there are five left

Thus, there are 5 more angles have a measure of 48°.

Answer 2

If there are twelve angles created, almost all of them are congruent. All the sides have to equal 180. If there are three parallel lines they must have 2 angles on each side. 3*2=6, there is a total of six with a measure of 48.