Question

Lines L and M are parallel. Lines t^1 and t^2 are transversals. What is m<1 if m<4=65*? Justify your answer. (Ps- there isn’t any options)

Answer 1

Answer: The measure of angle 1 is 115°.

Step-by-step explanation: Given that lines l and m are parallel and
`t_1` and
`t_2` are transversals.

We are to find the measure of angle 1 if measure of angle 4 is 65°.

Given that

`m\angle 4=60^\circ.`

That is, transversal
`t_2` is inclined at angle of 65° to line m, so it must inclined at angle of 65° to line l, because the angles will be corresponding.

Also, since ∠1 and the angle with measure 65° makes a linear pair, so we get

`m\angle 1+65^\circ=180^\circ\\\\\Rightarrow m\angle 1=180^\circ-65^\circ\\\\\Rightarrow m\angle 1=115^\circ.`

Thus, the measure of angle 1 is 115°.

Answer 2

As lines l and m are parallels, therefore, alternate interior angles are congruent,
then:
From the figure, m∠2 and m∠4 are alternate interior angles:
Hence,
m∠4 = 65°
m∠4 = m∠2
and,
m∠2 = 65°

Now,
The m∠1 and m∠4 are supplementary, therefore,

m∠1 + m∠4 = 180°

m∠1 + 65° = 180°

m∠1 = 180° - 65°

m∠1 = 115°