Looking at problem 1: m∠ABE
We are given a diagram with point E inside angle ABC, and rays from B to A, B to C, and B to E. There are perpendiculars drawn from E to BA and BC — marked with right-angle symbols. Also, the segments from E to those sides are marked as equal (with tick marks). This tells us that E is equidistant from the two sides of angle ABC, which means BE is the angle bisector of ∠ABC.
We’re told that ∠EBC = 43°. Since BE bisects ∠ABC, then ∠ABE must also be 43°.
So, m∠ABE = 43°
Let me double-check: The key here is recognizing that if a point is equidistant from the two sides of an angle, it lies on the angle bisector. That’s the Angle Bisector Theorem converse. So yes, since E is equidistant from BA and BC, BE splits ∠ABC into two equal parts. One part is 43°, so the other must be too.
Final Answer:
43°
Parent Tip: Review the logic above to help your child master the concept of bisecting angles worksheet.
