Step-by-step explanation:
Statement Reason
BA and BC opposite rays Given
AC is a straight line Definition of opposite rays
∠ABD + ∠CBD = ∠ABC Angle addition postulate
∠ABD + ∠CBD = 180° Definition of linear pair
m∠ABD = 5x + 7 Given
m∠CBD = 9x + 19 Given
5x + 7 + 9x + 19 = 180 Substitution property of equality
14x = 180 - 26 Subtraction property of equality
x = 154/14 Division property of equality
x = 11 Proved
