Question

What are the measures of ∠1, ∠2, and ∠3? Enter your answers in the boxes.

m∠1 = °, m∠2 = °, m∠3 = °

Answer 1

Answer: m<1 is 60, m<2 is 60, and m<3 is 120

Step-by-step explanation:

M<1 is 60 and m<2 is also 60 because the interior triangle angles have to equal 180 so M<1 + m<2 + 60 = 180 so m<1 and m<2 are both sixty.

m<3 is 120 because m<2 and m<3 are supplementary so if a supplementary angle is equal to 180 then m<2 + m<3 = 180 and m<2 is 60 so m<3 is 120.

Answer 2

The required measures of angles ∠1 = 59°, ∠2 = 61° and ∠3 = 119°

Intersecting Lines:

If two or more line intersecting in any plane then interior angles, exterior angles, line pair angles and corresponding angles are made.

How to calculate measures of the angles ?

On the observation of given parallel lines and their intersecting lines we have

At lowest intersection point

∠4 + 60° + 61° = 180°

∠4 = 59°

Now

∠4 = ∠1  = 59° alternate interior angles

Using the triangle sum property

∠1  + ∠2 + 60° = 180°

59° + ∠2 + 60° = 180°

∠2 = 61°  This is also alternate interior angles

Also we have

∠2 + ∠3 = 180°

61° + ∠3  = 180°

∠3 = 119°

This is the conclusion to the answer.

Learn more about intersecting lines here-

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