Question

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

Answer 1

m∠EBC=34°

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°