Answer/Step-by-step explanation:
a. Vertex of <4 is the endpoint where the 2 rays meet to form <4.
Vertex of <4 is point B.
b. Sides of <1 are rays BD and BC.
c. Another name for <5 is <DBE.
d. <FBC is a right angle. (BF meets AC at 90°)
e. <EBF is an obtuse angle. (It is greater than 90° but less than 180°)
f. <ABC is a straight angle. (It measures 180°)
g. An angle bisector is ray BE
h. m<EBD = 36°
m<DBC = 108°
m<EBD + m<DBC = m<EBC (angle addition postulate)
36 + 108 = m<EBC (Substitution)
144° = m<EBC
m<EBC = 144°
i. m<EBF = 117°
m<ABE + m<ABF = m<EBF (angle addition postulate)
m<ABE + 90° = 117° (Substitution)
m<ABE = 117 - 90
m<ABE = 27°
2. m<MKL = 83°,
m<JKL = 127°,
m<JKM = (9x - 10)°
m<JKM + m<MKL = m<JKL (angle addition postulate)
(9x - 10)° + 83° = 127° (substitution)
Solve for x
9x - 10 + 83 = 127
9x + 73 = 127
9x + 73 - 73 = 127 - 73
9x = 54
9x/9 = 54/9
x = 6
3. m<EFH = (5x + 1)°
m<HFG = 62
m<EFG = (18x + 11)
m<EFH + m<HFG = m<EFG (angle addition postulate)
5x + 1 + 62 = 18x + 11 (substitution)
5x + 63 = 18x + 11
5x - 18x = -63 + 11
-13x = -52
-13x/-13 = -52/-13
x = 4
m<EFH = (5x + 1)°
Plug in the value of x
m<EFH = 5(4) + 1 = 21°
m<EFG = (18x + 11)
Plug in the value of x
m<EFG = 18(4) + 11 = 72 + 11
m<EFG = 83°
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) [tex]\overrightarrow{BD}[/tex] and [tex]\overrightarrow{BC}[/tex]
c) ∠EBD
d) ∠FBC = Right angle
e) ∠EBF = An obtuse angle
f) ∠ABC = Straight angle
g) [tex]\underline{\overrightarrow{EB}}[/tex]
h) m∠EBC = 180°
i) 36°
2) x = 6°
3) x = 4°
a) The vertex of an angle is the point where the lines forming the angles meet.
b) The sides of an angle are the rays that form the angle.
c) The name of an angle can be given by the three points of the angle
Therefore;
d) Given that [tex]\overrightarrow{BF}[/tex] ⊥ [tex]\overleftrightarrow{AC}[/tex], we have;
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 [tex]\mathbf{\overrightarrow{EB}}[/tex] bisects ∠ABD
Which gives;
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;
i) m∠EBF = 117°
m∠EBF = m∠ABE + m∠ABF
m∠ABF = m∠FBC = 90°
Therefore;
117° = m∠ABE + 90°
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
[tex]x = \dfrac{54 ^{\circ}}{9} = \mathbf{6^{\circ}}[/tex]
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
[tex]x = \dfrac{52^{\circ}}{13} = \mathbf{4^{\circ}}[/tex]
Learn more about angle addition property here:
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