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3 years ago

PLEASE HELP ME!!! Please help me find the measure of AEC, and please show all work. Thanks :)))

Mathematics

2 answers:

Scrat [10]3 years ago

8 0

Given: ∠AEB = 11x - 12, ∠CED = 4x + 1, Line EC bisects ∠BED

To find: ∠AEC

Since Line EC bisects ∠BED, ∠BEC = ∠CED

That is: ∠BEC = 4x + 1

Therefore ∠BEC + ∠CED = 4x + 1 + 4x + 1 = 8x + 2

Now, ∠AEB = 11x - 12

Therefore: ∠AEB + ∠BEC = ∠AEC

That is, 11x - 12 + 4x + 1 = ∠AEC

∠AEC = 15x - 11

Therefore ∠AEC = 15x - 11

Hopeit helps :)

USPshnik [31]3 years ago

3 0

∠BEC ≅ ∠CED definition of angle bisector

∠BEC = ∠CED definition of congruency

∠AEB , ∠BEC, and ∠CED are supplementary

∠AEB + ∠BEC + ∠CED = 180 definition of supplementary angles

∠AEB + ∠CED + ∠CED = 180 substitution

11x - 12 + 4x + 1 + 4x + 1 = 180 substitution

19x - 10 = 180 simplified (added like terms)

19x = 190 addition property of equality

x = 10 division property of equality

*****************************************************************

∠AEB = 11x - 12

= 11(10) - 12

= 110 - 12

= 98

∠BEC = ∠CED = 4x + 1

= 4(10) + 1

= 40 + 1

= 41

********************************************************************

∠AEB + ∠BEC = ∠AEC segment addition property

98 + 41 = ∠AEC substitution

139 = ∠AEC simplified (added like terms)

Answer: 139°

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