Answer:
10. (a) x = 22
11. 1, 4 -- given; 2, 5 -- definition of angle bisector; 3 -- reflexive property; 6 -- ASA postulate
Step-by-step explanation:
10.
The marked angles are supplementary. (The two base angles are congruent, and the exterior angle is supplementary to the unmarked base angle.) That means you have ...
(5x -40)° +(5x)° = 180°
10x -40 = 180 . . . . . . . . . . divide by °, collect terms
x -4 = 18 . . . . . . . . . . . . . divide by 10
x = 22 . . . . . . . . . . . . . add 4
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11.
Normally, the given statements are collected at the beginning of the proof. This one is different. It addresses one angle, the shared side, and then the other angle, before claiming ASA congruence.
Reasons 1, 4: Given
Reasons 2, 5: Definition of angle bisector
Reason 3: Reflexive property of congruence
Reason 6: ASA congruence postulate
