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) â EBD
d) â FBC = Right angle
e) â EBF = An obtuse angle
f) â ABC = Straight angle
g) Â
h) mâ 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 â 4 = Point B
b) The sides of an angle are the rays that form the angle.
The sides of â 1 =
c) The name of an angle can be given by the three points of the angle
Therefore;
Another name of angle â 5 is â EBD
d) Given that ⼠, we have;
â FBC = 90° = Right angle
e) â EBF = An obtuse angle
f) â ABC = 180° = Straight angle
g) Given that by symbol for equal angles in the diagram, we have;
â EBD = â ABE
Therefore, segment bisects â ABD
Which gives;
An angle bisector is
h) mâ EBD = 36°, mâ DBC = 108°
mâ EBC = mâ ABE + mâ EBD + mâ DBC Â (angle addition property)
mâ EBC = mâ EBD + mâ EBD + mâ DBC (substitution property)
Therefore;
mâ EBC = 36° + 36° + 108° = 180°
i) mâ EBF = 117°
mâ EBF = mâ ABE + mâ ABF
mâ ABF = mâ FBC = 90°
Therefore;
117° = mâ ABE + 90°
mâ ABE = 117° - 90° = 27°
2. Given:
mâ MKL = 83°, mâ JKL = 127°, mâ JKM = (9¡x - 10)°
Required:
The value of x
Solution:
mâ JKL = mâ MKL + mâ 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. mâ EFH = (5¡x + 1)°
mâ HFG = 62°
mâ EFG = (18¡x + 11)°
By angle addition property, we have;
mâ EFG = mâ EFH + mâ 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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