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cupoosta [38]
2 years ago
15

in the diagram below, <AFB = <EFD. if m<EFD = (5x+6)°, m<DFC = (19x-15)°, and m<EFC = (17x+19)°, find m<AFE​

Mathematics
1 answer:
NeX [460]2 years ago
3 0

Answer:

m<AFE​ =  128°.

Step-by-step explanation:

<u>Step 1: Find the value of x</u>

<em>Angle EFD + Angle DFC = Angle EFC</em>

5x + 6 + 19x - 15 = 17x + 19

24x - 9 = 17x + 19

7x = 28

x = 4

<u>Step 2: Find all angles</u>

<em>Angle AFB=Angle EFD= 5x + 6</em>

5(4) + 6 = 26°

Angle DFC = 19x - 15

19(4) - 15 = 61°

<u>Step 3: Find angle AFE</u>

<em>Line BD is a straight line and all angles on a straight line are equal to 180°.</em>

<em>Angle AFB + Angle AFE + Angle EFD = 180°</em>

26 + BFC + 26 = 180°

BFC = 180 - 52

BFC = 128°

<em>Therefore, m<AFE​ is equal to 128°.</em>

!!

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