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Tresset [83]
2 years ago
15

If mAD = (17x + 2)°, mAC = (7x - 10°), and m∠ABC = (4x + 15)°, find m∠ABC Please help

Mathematics
1 answer:
goldenfox [79]2 years ago
4 0

Answer:

m<ABC  = 51degrees

Step-by-step explanation:

The angle at the vertex is half the difference of the angles at the intercepted arcs. Hence;

m<B = 1/2 (arcAD - arcAC)

<ABC = 1/2(17x + 2 -(7x - 10°))

4x + 15 = 1/2(17x-7x+2+10)

2(4x+15) = 10x+12

8x + 30 = 10x+12

8x-10x = 12-30

-2x = -18

x = 18/2

x = 9

Get m<ABC

m<ABC = 4x + 15

m<ABC = 4(9) + 15

m<ABC = 36 + 15

m<ABC  = 51degrees

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x = 5

<u>explanation</u>

70 + 23x - 5 + 110 + 14x = 360

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