Question

In the diagram below, start overline, B, D, end overline, \parallel, start overline, A, E, end overline, comma BD ∥ AE , start overline, B, F, end overline BF bisects angle, A, B, D, comma∠ABD, m, angle, E, equals, 36, degreesm∠E=36 ∘ and m, angle, B, F, E, equals, 118, degrees, .m∠BFE=118 ∘ . Find m, angle, C, .m∠C.

Answer 1

To find the measure of angle C, use the angle addition postulate: m angle C = m angle ABE - m angle BFE. Given the measures of angle BFE and angle ABE, substitute these values to find m angle C.

Step-by-step explanation:

To find the measure of angle C, we will use the angle addition postulate. Since angle BFE and angle ABD are adjacent angles, their measures add up to the measure of angle ABE. Therefore, m angle C = m angle ABE - m angle BFE. Given that m angle BFE is 118 degrees and m angle ABE is 36 degrees, we can substitute these values and find that m angle C is equal to 36 degrees - 118 degrees which is equal to -82 degrees.

Answer 2

Answer:
ZE = 38°
Step-by-step explanation:
You want the measure of angle E in the triangle shown.
Linear pair
Angle BFA and the one marked 118° form a linear pair, so are supplementary.
¿BFA = 180° -118° = 62°
Alternate interior angles
Transversal BF lies between parallel lines
BD and AE, creating alternate interior angles BFA and FBD. These are congruent, so...
Angle bisector
BF bisects angle ABD, so angle ABD is twice the measure of angle FBD:
LABD = 2X_FBD = 2×62° = 124°
Exterior angle
Angle ABD is an exterior angle to triangle
BCD, so is equal to the sum of the remote interior angles:
LABD = BCD + CDB
Then the acute angle at D is ...
LCDB = LABD -BCD = 124° -86° = 38°
Corresponding angles
Transversal CE crosses parallel lines BD and AE, so the corresponding angles it creates are congruent. This means ...
ZE = LCDB = 38°
The measure of angle E is 38°.
Additional comment
You can also find angle A = 56° using the sum of angles in triangle ABF, then angle E using the sum of angles in triangle ACE.
The result is the same. The number of math operations is slightly more. The number of geometric relations you need to invoke for that is probably smaller.
In short, the more familiar you are with the geometric relationships, the less work you have to do.
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