Question

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Answer 1

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°