Question

The diagram shown below is not drawn to scale. If m∠CBA=2x+2, m∠DBC=42°, and m∠DBA=6x-24, then find the numerical value of m∠DBA.

Answer 1

DBA = 6x - 24

DBC = 42

CBA = 2x + 2

DBA = ?

DBA = DBC + CBA

Substitution

6x - 24 = 42 + 2x + 2

Simplification

6x - 2x = 42 + 2 + 24

4x = 68

Solve for x

x = 68 / 4

x = 17

Find DBA

DBA = 6(17) -24

DBA = 102 - 24

DBA = 78°

RESULT DBA = 78°