Question

Find the value of a and b, if b = 2a.​

Answer 1

a=50°,b=100°

angle BCE=angleDCF =30°

angleFDC=angleBEC=a (by construction, alternate interior angle)

In triangle FDC, we know that

angleF+angleD+angleC=180°

b+a+30=180°

2a+a=180-30°(b=2a)

3a=150°

a=50°

b=2a=100°

hope you understand

Answer 2

Answer:

a=40° b=80°

Step-by-step explanation:

∠ADC + ∠ABC = 180° [Opposite angles of cyclic quadrilateral]

∠ADC + ∠FDC = 180°

∠FDC = ∠ABC

∠CBE = ∠ADC

∠FDC + ∠CBE = 180°

∠FCD = 30° [Vertically opposite angles]

∠a + ∠CBE = 150°

∠b + ∠FDC = 150°

2∠a + ∠FDC = 150°

∠a + CBE + 2∠a + ∠FDC = 300°

3∠a + 180° = 300°

3∠a = 120°

∠a = 40°

∠b = 80°