Math question, geometry, fill in the blanks. me

a||bGiven∠1≅∠2definition of corresponding anglesm∠1=m∠2corresponding angles are congruent∠2 and ∠3 are supplementarydefinition of linear pairm∠2+m∠3=180°If two angles form a linear pair, their angle measures to 180°m∠1+m∠3=180°proved earlier m∠1=m∠2

Step-by-step explanation:

In geometry, transversal is a line which cuts 2 or more lines, often parallel lines.

When lines are cut by a transversal,

angles which occupy same relative position are termed as corresponding angles. If the lines are parallel then corresponding angles are congruent.pairs of angles on either side of transversal are termed as alternate interior angles. If the lines are parallel then alternate interior angles are congruent.If lines are parallel, then pairs of consecutive interior angles formed are supplementary

It is given that, a||b

By the definition of corresponding angles,

∠1≅∠2

⇒m∠1=m∠2(as corresponding angles are congruent when parallel lines are cut by a transversal)

∠2 and ∠3 are supplementary, as they form a linear pair

⇒m∠2+m∠3=180°(If two angles form a linear pair, their angle measures sum to 180°)

⇒m∠1+m∠3=180° (m∠1=m∠2 as we have proved above)

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