1) ∠5 and ∠6 are supplementary angles not vertical angles this statement is false.
2) ∠2 and ∠7 are alternally interior angles yeah that statement is true.
3) ∠2 and ∠4 are supplementary angles no they are not complementary, because sum of those two angles i.e. ∠2+∠4 =180.
Certainly! When lines t and u are parallel and intersected by a transversal s, several pairs of angles are formed. The most common angle relationships are based on the corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles. Here are the step-by-step explanations:
Corresponding Angles:
Corresponding angles are in the same position relative to the transversal on the same side of the lines.
If t and u are parallel, corresponding angles are equal For example, if ∠1 is a corresponding angle to ∠2, then
∠1= ∠2.
Alternate Interior Angles:
Alternate interior angles are on opposite sides of the transversal and inside the parallel lines.
If t and u are parallel, alternate interior angles are equal.
For example, if ∠3 is an alternate interior angle to ∠4, then ∠3=∠4
Alternate Exterior Angles:
Alternate exterior angles are on opposite sides of the transversal and outside the parallel lines.
If t and u are parallel, alternate exterior angles are equal.
For example, if ∠5 is an alternate exterior angle to ∠6
Consecutive Interior Angles:
Consecutive interior angles are on the same side of the transversal and inside the parallel lines.
If t and u are parallel, consecutive interior angles are supplementary (their sum is 180∘)
For example, if ∠7 is a consecutive interior angle to ∠8, then ∠7+∠8 - ¹⁸⁰ᵒ
These angle relationships are fundamental in geometry when working with parallel lines and transversals. They help solve problems involving angles and prove theorems about the geometric properties of parallel lines.