Question

In the diagram below, AB || DF, m/DCE = 103° and m/CEF = 145°. Find m/B.Step12tryAnglem/DCE = 104°-m/CEF = 145°m/Select a ReasonReasonGivenGiven

Answer 1

Angle m/ACB is equal to angle m/DCE, which is 103°. Angle m/BCF is equal to angle m/CEF, which is 145°. Subtract the measures of angle m/ACB and angle m/BCF from 180° to find m/B, which equals -68°.

Step-by-step explanation:

To find m/B, we need to use the properties of parallel lines and alternate interior angles.

Since AB || DF, the angle m/DCE and angle m/CEF are alternate interior angles.

Using this information, we can find the measure of angle m/B.

First, we know that m/DCE = 103°. Since AB || DF, angle m/DCE and angle ACB are alternate interior angles.

Therefore, m/ACB = m/DCE

= 103°.

Next, we know that m/CEF = 145°. Again, since AB || DF, angle m/CEF and angle BCF are alternate interior angles. Therefore, m/BCF = m/CEF

= 145°.

Now, we can find m/B by subtracting the measures of angle m/ACB and angle m/BCF from 180°, since they form a straight line. m/B = 180° - m/ACB - m/BCF

= 180° - 103° - 145°

= 180° - 248°

= -68°.