Answer:
C. 66°
Step-by-step explanation:
Given:
m∠FAB = 48°,
m∠ECB = 18°,
Required:
m∠ABC
SOLUTION:
∠CHB ≅ ∠FAB (alternate interior angles theorem)
m∠CHB = ∠FAB
m∠CHB = 48° (substitution)
m∠CHB + m∠ECB + m∠CBH = 180° (sum of angles in a ∆)
48° + 18° + m∠CBH = 180° (substitution)
66° + m∠CBH = 180°
Subtract 66° from each side
m∠CBH = 180° - 66°
m∠CBH = 114°
Thus,
m∠CBH + m∠ABC = 180° (Linear pair)
114° + m∠ABC = 180° (substitution)
Subtract 114° from both sides
m∠ABC = 180° - 114°
m∠ABC = 66°
The angle m∠ABC will be equal to 66° the correct answer is option C.
The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.
Given:
m∠FAB = 48°,
m∠ECB = 18°,
Required:
m∠ABC
The angle ABC will be calculated as follows:-
∠CHB ≅ ∠FAB (alternate interior angles theorem)
m∠CHB = ∠FAB
m∠CHB = 48° (substitution)
m∠CHB + m∠ECB + m∠CBH = 180° (sum of angles in a ∆)
48° + 18° + m∠CBH = 180° (substitution)
66° + m∠CBH = 180°
Subtract 66° from each side
m∠CBH = 180° - 66°
m∠CBH = 114°
Thus,
m∠CBH + m∠ABC = 180° (Linear pair)
114° + m∠ABC = 180° (substitution)
Subtract 114° from both sides
m∠ABC = 180° - 114°
m∠ABC = 66°
Therefore the angle m∠ABC will be equal to 66° the correct answer is option C.
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