PLEASE HELP! I NEED GOOD ANSWERS PLEASE!
a. What is the relationship between ∠FEB and ∠ABE?
b. What are the two parallel lines in this diagram?
c. What are the two transversals?
d. Find m∠ABE.
e. Find m∠ABF.
f. Find m∠EBF. How did you find this?
f. . Find m∠FBC. How did you find this?
Answers
a. <FEB and <AEB are alternate interior angles
b. AC and DG are parallel lines
c. EB and BF are the transversals
d. <ABE and <FEB are alternate interior angles, meaning that their angle measures are congruent, thus <ABE = <FEB = 45
e. <GFB and <ABF are alternate interior angles, meaning that their angle measures are congruent, therefore <ABF = 110
f. <GFB is a remote angle to triangle EBF. Remote angles are formed when one extends one of the sides of a triangle, the remote angle is found between the extension of the side and a side of the triangle. The remote angles theorem states that the sum of the two non-adjacent angles equals the remote angle. Applying this here one can state the following,
<FEB + <FBE = <GFB
45 + <FBE = 110
<FBE = 65
f. <FBC and <GFB are same-side interior angles, this means that the two angles are supplementary, their angle measures add up to 180. Apply this property here,
<GFB + <FBC = 180
110 + <FBC = 180
<FBC = 70
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=============================================================
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