Answer :
Based on triangle ABC, each measure include the following:
10. CB = 45.
11. FE = 28.5
12. m∠DFC = 64°
13. AE = 30
14. m∠DFB = 71°.
15. DF = 30
What is a midsegment?
In Mathematics and Euclidean Geometry, a midsegment is a type of line segment that is used for connecting the midpoints of two sides of a triangle. Also, the midsegment of a triangle is one-half the length of its parallel base.
By applying the midsegment theorem, we can determine each of the lengths and angles as follows:
CB = 2DE
CB = 2(22.5)
CB = 45.
Part 11.
FE = AC/2
FE = 57/2
FE = 28.5
Part 12.
m∠EDF ≅ m∠DFC (Alternate interior angles theroem)
m∠DFC = 64°
Part 13.
AE = AB/2
AE = 60/2
AE = 30
Part 14.
By applying sine rule, we have:
sinx/22.5 = sin64/28.5
sinx = 22.5 × 0.0315
x = sin⁻¹(0.7096)
x = 45.20
m∠DFB = 180 - (64 + 45.20)
m∠DFB = 70.8 ≈ 71°.
Part 15
DF ≡ AE = 30
Read more on midsegment here: brainly.com/question/14981061
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