Question

Consider the figure & find a + b + g if $\frac{\alpha}{2}$ = $\frac{\beta}{3}$ = $\frac{\gamma}{2}$

• A. 100⁰
• B. 120⁰
• C. 140⁰
• D. 210⁰

Answer 1

Answer: (C)

140⁰

Answer 2

ΠF = a + g & ΠD = Πb + g

Quadrilateral AFED is cyclic

ή ΠF + ΠD = 180⁰ ή a + b + 2g = 180⁰

ή 2k + 3k + 4k = 180⁰ $\left\{ let\frac{\alpha}{2} = \frac{\beta}{3} = \frac{\gamma}{2} = k \right\}$

ή k = 20⁰

ή a + b + g = 7k = 140⁰