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x = 40

m<AFE = 140

m<BFD = 140

Step-by-step explanation:

1. Finding X

As one can see, AD is a straight line (hence the three angles that add up to is equal 180 degrees). It is given that m<CFD is 90 degrees (signified by the box).

Given;

AD - straight line

m<AFB + m<BFC + m<CFD = 180

( m<AFB, m<BFC, m<CFD form line AD, the degree measures in al ine equal 180, hence m<AFB + m<BFC + m<CFD = 180)

m<BFC = 50

m<CFD = 90 (signified by box around it)

m<AFB + m<BFC + m<CFD = 180                   parts whole postulate

x + 50 + 90 = 180                                             substitution

x + 140 = 180                                                     algebra

x = 40

2. Finding m<AFE and m<BFD

When two straight lines intersect, four angles are formed. The angles that are opposite to each other are called vertical angles, and vertical angles are congruent in other words, have the same measure.

Given;

m<BFD = m< AFE

m<BFC + m<CFD = m<BFD

m<BFC = 50

m<CFD = 90

m<BFC + m<CFD = m<BFD                           Given (parts whole postulate)

50 + 90 = m<BFD                                           substitution

140 = m<BFD                                                  algebra

140 = m<BFD = m<AFE                                  substition

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