Question

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Answer 1

x = 40

m<AFE = 140

m<BFD = 140

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

Answer 2

What is the value of x?

x = 40 degrees.

What is the measure of angle AFE?

Angle AFE = 140 degrees

What is the measure of angle BFD?

Angle BFD = 140 degrees.

Explanation:

Angle AFC is 90 degrees.

To find angle x, we have to subtract angle BFC.

90 - 50 = 40 degrees.

Line BFE is 180 degrees.

To find angle AFE, we have to subtract angle x from 180 degrees.

We have solved x already.

180 - 40 = 140 degrees.

Angle BFD is just 90 degrees plus 50 degrees.

90 + 50 = 140 degrees.