Line I is parallel to line m. If the measure of <6 is 75, what is the measure of <3

In the given diagram, the measure of ∠3 is 105°

From the question,

We are to determine the measure of ∠3

In the diagram, ∠3 and ∠6 are consecutive interior angles

NOTE:

If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary

That is,

∠3 + ∠6 = 180°

From the given information,

∠6 = 75°

Then, we can write that

∠3 + 75° = 180°

∠3 = 180° - 75°

∠3 = 105°

Hence, the measure of ∠3 is 105°

Learn more on finding the measures of angles here: link

m∠3 = 105°

Step-by-step explanation:

Line 'l' is parallel to line 'm' and a transversal is intersecting these parallel lines at two distinct points.

m∠3 + m∠6 = 180° [Consecutive interior angles]

Since, ∠6 = 75° [Given]

m∠3 + 75° = 180°

m∠3 = 180 - 75

        = 105°

Therefore, measure of ∠3 is 105°.

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