m<ABE=2n+7and m<EBF=4N-13, find the measure of angle ABE

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2 Answers

The question doesn’t state where F is in relation to A, B or E, so we have to guess. Here are two guesses.

 

If ABF is a straight line then ∠ABE+∠EBF=180, so 2n+7+4n-13=180, 6n-6=180.

Divide each side by 6: n-1=30 so n=31 and m∠ABE=2n+7=2×31+7=62+7=69°.

 

If BF bisects ∠ABE, then ∠ABE=2×∠EBF, so 2n+7=2(4n-13)=8n-26. So 6n=33 and, dividing both sides by 3: 2n=11. Therefore m∠ABE=2n+7=11+7=18°.

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