Question

Angle Number
Measure
1
2
13
1
1267
2
3

Answer 1

∠1=54°

∠2=54°

∠3 = 126°

Explanation:

We need to find ∠1, 2 and 3

Since a traversal cut parallel lines we would use supplementary angles , congruent angles rules to solve the problem.

Angle 1 and 126 are supplementary angles.

They add up to make 180

So, ∠1 + 126 = 180

∠1 = 180-126

∠1 =54

We get ∠1=54°

Now, ∠1 ≅ ∠2, because they are corresponding angles and if traversal cut parallel lines, corresponding angles are congruent.

So ∠1 ≅ ∠2 therefore, ∠2=54°

Now, for finding measure for ∠3, we know that 126 and ∠4 are corresponding angles and corresponding angles are congruent.

So, ∠4 = 126°

We know that ∠3 and ∠4 are vertical angles.

And if traversal cut parallel lines, vertical angles angles are congruent.

So, ∠3 = 126°