Answer:
m∠DBC is 43°
Step-by-step explanation:
Let us solve the question
∵ D is in the interior of ∠ABC
→ That means D divides ∠ABC into two angles ABD and DBC
∴ m∠ABD + m∠DBC = m∠ABC
∵ m∠ABD = (3x + 5)°
∵ m∠DBC = (5x - 7)°
∵ m∠ABC = 78°
→ Substitute them in the equation above
∴ 3x + 5 + 5x - 7 = 78
→ Add the like terms in the left side
∵ (3x + 5x) + (5 + -7) = 78
∴ 8x + -2 = 78
∴ 8x - 2 = 78
→ Add 2 to both sides
∴ 8x -2 + 2 = 78 + 2
∴ 8x = 80
→ Divide both sides by 8
∴ x = 10
→ To find m∠DBC, substitute x by 10 in its measure
∵ m∠DBC = 5(10) - 7
∴ m∠DBC = 50 - 7
∴ m∠DBC = 43°
