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zheka24
1 month ago
13

If m<DBC=(12x-3)°, m<DBE=(5x+12)°, and m<EBC=(3x+13)°, find m<EBC.

Mathematics
1 answer:
Leona [12.6K]1 month ago
8 0

Answer:

m∠EBC=34°

Step-by-step explanation:

We establish that

m∠DBC=m∠DBE+m∠EBC

Refer to the accompanying diagram for clarity on the issue

Replace the known values in the equation and determine x

(12x-3)\°=(5x+12)\°+(3x+13)\°\\12x-3=8x+25\\12x-8x=25+3\\4x=28\\x=7

Calculate the size of angle EBC

m∠EBC=(3x+13)°

Insert the value for x

m∠EBC=(3(7)+13)°

m∠EBC=(21+13)°

m∠EBC=34°

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