Math Problem Statement
In the figure, BA−→BA→ and BC−→−BC→ are opposite rays. BH−→−BH→ bisects ∠EBC∠EBC and BE−→BE→ bisects ∠ABF∠ABF.
If m∠EBC=(3r+10)°m∠EBC=3r+10° and m∠ABE=(2r−20)°m∠ABE=2r-20°, find m∠EBFm∠EBF.
Solution
We are given the following information:
- and are opposite rays, meaning .
- bisects , meaning .
- bisects , meaning .
Information about the angles:
Step 1: Express
Since ( \overrightarrow{
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Math Problem Analysis
Mathematical Concepts
Geometry
Angle Bisectors
Linear Pair of Angles
Formulas
Sum of angles on a straight line: ∠ABC = 180°
Angle bisector property: m∠EBC = 2 × m∠HBC, m∠ABF = 2 × m∠ABE
Theorems
Linear Pair Theorem
Angle Bisector Theorem
Suitable Grade Level
Grades 9-10
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