Question

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

Answer 1

Answer:

m∠EBC=34°    

Step-by-step explanation:

we know that  

m∠DBC=m∠DBE+m∠EBC

see the attached figure to better understand the problem

substitute the given values in the formula and solve for x

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

Find the measure of angle EBC

m∠EBC=(3x+13)°

substitute the value of x      

m∠EBC=(3(7)+13)°

m∠EBC=(21+13)°    

m∠EBC=34°