Answer:
To start with, if we assume you already know all the angle relationships, then you must understand that by using *(just)* the following 5 "angle relationships" we can find all angle measures (considering that we already have two):
*The following examples must be applied to those on the same line/ transversal*
Vertical Opposite angles: They are the opposite angles that form when two lines intersect/ meet each other at a point. They're also congruent/ equal. Examples include: m∠10 & m∠16. (OR m∠3 & m∠5)
Linear pairs: They are supplementary/ can add up to 180°, are 2 angles/ a pair of ADJACENT angles on the same transversal, and share the same common vertex. Examples include: m∠10 & m∠11. (OR m∠6 & m∠15)
Corresponding angles: They are angles found in the exact same relative position but on different intersections. They're also congruent. Examples include: m∠1 & m∠3. (OR m∠16 & m∠6)
Alternate Interior: They are angles on opposite sides of a transversal between (interior, inside) the two intersecting lines. They are congruent angles.
Alternate Exterior: Similar to the "Alternate Interior", they are also angles that are OUTSIDE (exterior, outer) the two intersecting lines.
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Finding the measurement of each angle:
Starting with Linear Pairs: (SUBTRACT 180° BY THE GIVEN ANGLE, they are supplementary!)
TRANSVERSAL t:
If m∠10 equals 135°, then m∠ 11 equals: 45° (180° - 135°)
Transversal m:
If m∠12 equals 75°, then ∠1 equals 105° (180 - 75)
OR
If m∠12 equals 75°, then ∠13 equals 105° too.
Second, Vertical Opposite angles: (ANGLES ARE CONGRUENT)
Transversal t:
If m∠10 equals 135°, then m∠16 equals 135°
If m∠11 equals 45°, then m∠9 equals 45°
Transversal m:
If m∠12 equals 75°, then m∠2 equals 75°
If m∠1 equals 105°, then m∠13 equals 105°
Third, Alternate interior angles: (ANGLES ARE CONGRUENT)
Transversal t:
If m∠9 equals 45°, then m∠15 equals 45°
If m∠16 equals 135°, then m∠8 equals 135°
Transversal m:
If m∠13 equals 105°, then m∠3 equals 105°
If m∠2 equals 75°, then m∠14 equals 75°
Fourth, Alternate Exterior angles: (ANGLES ARE CONGRUENT)
Transversal t:
If m∠10 equals 135°, then m∠6 equals 135°
If m∠11 equals 45°, then m∠7 equals 45°
Transversal m:
If m∠12 equals 75°, then m∠4 equals 75°
If m∠1 equals 105°, then m∠5 equals 105°
Fifth, Corresponding angles: (ANGLES ARE CONGRUENT)
Transversal t:
∠10, ∠8 & ∠16, ∠6 all equal 135° (for the obvious reasons)
∠11, ∠15 & ∠9, ∠7 all equal 45°
Finally, the angles we've managed to get:
∠1 = 105°
∠2 = 75°
∠3 = 105°
∠4 = 75°
∠5 = 105°
∠6 = 135°
∠7 = 45°
∠8 = 135°
∠9 = 45°
∠10 = 135°
∠11 = 45°
∠12 = 75°
∠13 = 105°
∠14 = 75°
∠15 = 45°
∠16 = 135°
Hope I helped ^^