The measure of an angle, that forms a known larger angle with another
known angle can be determined by angle addition postulate.
Correct responses:
1. a) Point B
b) 
and 
c) ∠EBD
d) ∠FBC = Right angle
e) ∠EBF = An obtuse angle
f) ∠ABC = Straight angle
g) 
h) m∠EBC = 180°
i) 36°
2) x = 6°
3) x = 4°
Methods by which the above values are obtained
a) The vertex of an angle is the point where the lines forming the angles meet.
The vertex of the angle ∠4 = Point B
b) The sides of an angle are the rays that form the angle.
The sides of ∠1 =
c) The name of an angle can be given by the three points of the angle
Therefore;
Another name of angle ∠5 is ∠EBD
d) Given that 
⊥ 
, we have;
∠FBC = 90° = Right angle
e) ∠EBF = An obtuse angle
f) ∠ABC = 180° = Straight angle
g) Given that by symbol for equal angles in the diagram, we have;
∠EBD = ∠ABE
Therefore, segment 
bisects ∠ABD
Which gives;
An angle bisector is
h) m∠EBD = 36°, m∠DBC = 108°
m∠EBC = m∠ABE + m∠EBD + m∠DBC (angle addition property)
m∠EBC = m∠EBD + m∠EBD + m∠DBC (substitution property)
Therefore;
m∠EBC = 36° + 36° + 108° = 180°
i) m∠EBF = 117°
m∠EBF = m∠ABE + m∠ABF
m∠ABF = m∠FBC = 90°
Therefore;
117° = m∠ABE + 90°
m∠ABE = 117° - 90° = 27°
2. Given:
m∠MKL = 83°, m∠JKL = 127°, m∠JKM = (9·x - 10)°
Required:
The value of x
Solution:
m∠JKL = m∠MKL + m∠JKM
Which by plugging in the values gives;
127° = 83° + (9·x - 10)°
127° - 83° = 44° = (9·x - 10)°
44° + 10° = 54° = 9·x
x = 6°
3. m∠EFH = (5·x + 1)°
m∠HFG = 62°
m∠EFG = (18·x + 11)°
By angle addition property, we have;
m∠EFG = m∠EFH + m∠HFG
Therefore;
18·x + 11 = 5·x + 1 + 62
18·x - 5·x = 62 + 1 - 11 = 52
13·x = 52
x = 4°
Learn more about angle addition property here:
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