1. BC bisects ∠ABC.
2. GH = 5.
3. y = 2.
4. m∠DBE = 32°.
Which ray is a bisector of ∠ABC?
BC is a bisector of ∠ABC. A bisector is a ray that divides an angle into two equal parts. In the diagram, BC divides ∠ABC into two angles of equal measure.
What is GH?
GH is 5. We can see this from the given information that DC = 5. Since BC is a bisector of ∠ABC, it divides DC into two segments of equal length. Therefore, GH = DC / 2 = 5 / 2 = 5.
What is the value of y?
The value of y is 2. We can see this from the given information that m∠(8y + 4)° = 7x + 6y. Substituting in y = 2, we get m∠(8 * 2 + 4)° = 7x + 6 * 2, which simplifies to m∠20° = 7x + 12. Since m∠20° is a known value, we can solve for x to get x = 4. Substituting back into y = 2, we get y = 2.
What is m∠DBE?
m∠DBE is 20°. We can see this from the given information that m∠DBE = m∠ABC - m∠FBA. Since BC is a bisector of ∠ABC, m∠ABC = 2 * m∠FBA. Substituting in m∠ABC = 2 * m∠FBA, we get m∠DBE = 2 * m∠FBA - m∠FBA = m∠FBA. From the given information, m∠FBA = 7x + 6y. Substituting in y = 2, we get m∠FBA = 7x + 12. Since x = 4, m∠FBA = 7 * 4 + 12 = 20 + 12 = 32°. Therefore, m∠DBE = m∠FBA = 32°.