∠1 = ∠2 + ∠8
∠2 = ∠8
∠3 = ∠5
∠4 = ∠3 + ∠7
∠5 = ∠3
∠6 = ∠2 + ∠8
To find the measures of the numbered angles in the given figure, let's use the properties of parallel lines and transversals.
∠1: This is an exterior angle formed by line t and line a. Exterior angles formed by a transversal and parallel lines are equal to the sum of the opposite interior angles. In this case, angle 1 is equal to the sum of angles 2 and 8.
∠2: This is an interior angle formed by line t and line a. Since line t bisects line a, angle 2 is equal to angle 8.
∠3: This is an interior angle formed by line t and line b. Since line t bisects line b, angle 3 is equal to angle 5.
∠4: This is an exterior angle formed by line t and line b. Exterior angles formed by a transversal and parallel lines are equal to the sum of the opposite interior angles. In this case, angle 4 is equal to the sum of angles 3 and 7.
∠5: This is an interior angle formed by line t and line b. Since line t bisects line b, angle 5 is equal to angle 3.
∠6: This is an exterior angle formed by line t and line a. Exterior angles formed by a transversal and parallel lines are equal to the sum of the opposite interior angles. In this case, angle 6 is equal to the sum of angles 2 and 8.