Answer:
Questions 1-5:
∠53°
∠115°
∠108°
∠73°
∠115°
Step-by-step explanation:
To find missing angles like this, it's good to establish angle relationships and their relating theorems.
*Note: These are not all angle relationships, but they are necessary for this worksheet.
Vertical angles are two opposite angles created by intersecting lines or line segments.
An example of this from the attached assignment is angle 5 and angle 10. They are created from the two same lines. Vertical angles are congruent, so they have equal measures.
Alternate interior angles are two angles formed when a line (called a transversal) passes through two parallel lines. They are angles on opposite sides of the transversal, and they exist inside the area between the parallel lines. An example of alternate interior angles is angle 15 and angle 14. Alternate interior angles are also congruent.
Alternate exterior angles are also formed by the intersection of a transversal and two parallel line. They are also on opposite sides of the transversal, but they are on the outside of each of the parallel lines. An example of these angles are angles 14 and angle 21.
Linear pairs form straight angles together, which means they are supplementary to one another and their sum equals 180°. There are such thing as linear triples which are three angles that sum up to 180, and they are also used in this worksheet.
Corresponding angles are formed on the same side of the transversal, and one angle is exterior wile the otehr is interior. The two angles are is the same orientation, and can be translated directly onto each other. They are congruent.
Now that we know this, let's go through angles 1-5.
Angle 1 is a linear pair with the angle measuring 127°. Angle 1 must equal 53 because it must add up to 180 when added to 127.
angle 2 is vertical angles with an angle measuring 115°. Since vertical angles are congruent, angle 2 also equals 115°.
Angle 3 is linear pairs with an angle measuring 73. Angle 3 then must be supplementary to that angle, making it 108°.
Angle 4 corresponds to the angle measuring 73°, so angle 4 also equals 73°.
Angle 5 is alternate interior angles with an angle 115°, so angle 5 must also equal 115°.
