The measure of angle CFD is The measure of angle CDF is The measure of angle AFB is The measure of angle BFD is The measure of angle ABC is

∠CDF = 23° ,  ∠CFD = 115° , ∠AFB = 115° , ∠BFD = 65° , ∠ABC = 42°

Step-by-step explanation:

m∠CDF = 180 - m∠CDE

m∠CDF = 180 - 157

m∠CDF = 23°

m∠CFD = 180 - ( m∠DCF + m∠CDF )

m∠CFD = 180 - ( 42 + 23 )

m∠CFD = 115°

m∠AFB = m∠CFD (Vertically opposite angles)

m∠AFB = 115°

m∠BFD = 180 - m∠CFD

m∠BFD = 180 - 115

m∠BFD = 65°

∠ABC

Solution 1:

m∠ABC = m∠DCF (Alternate angles)

m∠ABC = 42°

Solution 2:

In ΔAFB

m∠FAB = m∠CDF (Alternate angles)

m∠FAB = 23°

m∠ABC = 180 - ( m∠AFB + m∠FAB )

m∠ABC = 180 - ( 115 + 23 )

m∠ABC = 42°

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11

answer: x=3 and y=4

step-by-step explanation: