pls give step by step explanation
Answers
Answer:
∠ABC =130°. Please refer to the attachments to understand my answer better
Step-by-step explanation:
Solution 1:
Draw a ray CF parallel to ray BA, with transversal BC
∵ Ray BA is parallel to Ray DE
∵ Ray CF is parallel to Ray BA
∴ Ray CF is parallel to Ray DE
∵ Ray DE ║ Ray CF, DC is transversal
∴ ∠DCF = ∠EDC (Alternate angles)
m∠DCF = 100°
m∠BCF = m∠DCF - m∠DCB = 100-50 = 50
∵ BA║CF, BC is transversal
∴ ∠ABC and ∠BCF are Co-interior angles
∴ m∠ABC = 180 - m∠BCF
m∠ABC = 180 - 50
m∠ABC = 130°
Solution 2 :
Draw ray CF parallel to ray DE with transversal DC
∵ DE ║CF and DE║BA
∴ CF ║ BA
∵ CF ║ DE with transversal DC
∴ ∠EDC and ∠DCF are co-interior angles
∴ m∠DCF = 180 - m∠EDC
= m∠DCF = 180 - 100
m∠DCF = 80°
∵ CF ║ BA with BC transversal
∴ m∠ABC = BCF
m∠BCF = ∠DCF + BCD = 50+80 = 130°
∴ m∠ABC = 130°
