The three angles can be thought of as being supplementary, and
therefore, sum to 180°
The values and relationships are;
Reason:
Given;
m∠EBD = 58°
m∠DBC = 3·x - 5
m∠ABE = 2·x + 2
Solution:
(a) Given that m∠EBD, m∠DBC, and m∠ABE are adjacent angles forming a straight line, we have;
m∠EBD + m∠DBC + m∠ABE = 180° angles forming a straight line are
supplementary
Therefore;
58° + 3·x - 5 + 2·x + 2 = 180°
3·x + 2·x = 180 - 58 + 5 - 2 = 125
[tex]x = \dfrac{125}{5} = 25[/tex]
x = 25°
(b) m∠ABE = 2·x + 2
∴ m∠ABE = 2 × 25 + 2 = 52
m∠ABE = 52°
m∠ABD = m∠ABE + m∠EBD
∴ m∠ABD = 52° + 58° -= 110°
BE is a bisector of ∠ABD if m∠ABE = m∠EBD
m∠ABE = 52° < 58° = m∠EBD
∴ m∠ABE ≠ m∠EBD
Therefore;
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