Answer
Angle A = 40 degrees
Angle B = 80 degrees
Measure BCF = 120 degrees
Measure EFD = 60 degrees
Step-by-step explanation:
<u>Angle A:</u>
Ok, so we know angle A is congruent to angle D because of the line. If you make an equation out of it, you get 2x+20 = 3x+10. If you solve this equation:
2x + 20 = 3x + 10
20 = x+10
10 = x
you will get x=10. Plug it into the equation, and <u>Angle A = 40 degrees.</u>
<u>Angle B:</u>
The two lines that are both on angle B and E mean that they are congruent. We know that <u>angle E = 80 degrees, so angle B does too.</u>
<u>Measure BCF:</u>
We know that Angle A = 40 degrees, and angle B = 80 degrees. The degree sum of all angles in a triangle is 180 degrees.
80 + 40 = 120
180 - 120 = 60
<em>So measure BCA = 60 degrees.</em>
That angle is on a straight line. Two angles on a straight line add up to 180 degrees.
180 - 60 = 120.
So, <u>Measure BCF = 120 degrees.</u>
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<u>Measure EFD:</u>
We already found measure BCA while finding measure BCF, and that is just congruent to EFD.
So, <u>measure EFD = 60 degrees</u>
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