Answer :

saadhussain514
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° 

Answer:  The measure of angle 1 is 115°.

Step-by-step explanation:  Given that lines l and m are parallel and [tex]t_1[/tex] and [tex]t_2[/tex] are transversals.

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

Given that

[tex]m\angle 4=60^\circ.[/tex]

That is, transversal [tex]t_2[/tex] 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

[tex]m\angle 1+65^\circ=180^\circ\\\\\Rightarrow m\angle 1=180^\circ-65^\circ\\\\\Rightarrow m\angle 1=115^\circ.[/tex]

Thus, the measure of angle 1 is 115°.

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