ABCE is a cyclic quadrilateral. AED and BCD are straight lines. AC= CD, angle ABC= 45 degrees and angle ACE = 20 degrees. Work out angle ECD

∠ECD  is 110°

Step-by-step explanation:

For a cyclic quadrilateral,

∠ABC + ∠AEC = 180°

Therefore ∠AEC = 180° - 45° = 135°

∠CAE + ∠ACE + ∠AEC = 180° (Angles in a triangle)

Therefore ∠CAE =  180 - 20 - 135 = 25°

∠CAE = ∠CDA = 25° (Base angles of isosceles triangle ΔCAD)

∠CED + ∠AEC = 180°(Sum of angles on a straight line)

Therefore ∠CED + 135° = 180°

∠CED = 180° - 135° = 45°

∠ECD + ∠CED + ∠CDA = 180°

Therefore ∠ECD  = 180° - (∠CED + ∠CDA)

∠ECD  = 180° - (45° + 25°) = 110°

Therefore, ∠ECD  = 110°.

yes

step-by-step explanation:

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752