Question

Math question, Geometry, Fill in the blanks. Please help me

Answer 1

Answer:

1. a||b--------Given
2. ∠1≅∠2-------definition of corresponding angles
3. m∠1=m∠2------corresponding angles are congruent
4. ∠2 and ∠3 are supplementary-------definition of linear pair
5. m∠2+m∠3=180°-------If two angles form a linear pair, their angle measures to 180°
6. 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)