Answer:
The measure of angle ABE is 27°.
Explanation:
Consider the below figure attached with this question.
Given information: ∠ABE=2n+7 and ∠EBF=4n-13.
From the below figure it is clear that ∠ABE and ∠EBF are congruent.
[tex]m\angle ABE=m\angle EBF[/tex]
[tex]2n+7=4n-13[/tex]
Isolate variable terms on one side.
[tex]7+13=4n-2n[/tex]
[tex]20=2n[/tex]
Divide both sides by 2.
[tex]10=n[/tex]
The value of n is 10.
We need to find the measure of ∠ABE.
[tex]\angle ABE=2(10)+7=20+7=27[/tex]
Therefore, the measure of angle ABE is 27°.
The measure of angle ABE is 27°.
Since the angles are congruent, therefore, ∠ABE=2n+7 and ∠EBF = 4n-13 will be equated to each other.
This will be;
2n+7 = 4n-13
Collect like terms
4n-2n = 7+13
2n = 20
Divide both sides by 2.
2n/2 = 20/2
n = 10
Therefore, the value of n is 10.
Since angle ABE = 2n + 7
ABE = 2[10] + 7
= 20 + 7 = 27°.
Therefore, the measure of angle ABE is 27°
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