Complementary Angles 9C4F5A

1. \text{State the problem: We are given two complementary angles } \angle 1 \text{ and } \angle 2 \text{ with measures } m\angle 1=(3x-12)^\circ \text{ and } m\angle 2=(8x+3)^\circ. \text{ We need to find } m\angle 2.\n\n2. \text{Recall the definition of complementary angles: }\n$$m\angle 1 + m\angle 2 = 90^\circ.$$\n\n3. \text{Substitute the given expressions: }\n$$ (3x - 12) + (8x + 3) = 90.$$\n\n4. \text{Simplify the left side: }\n$$3x - 12 + 8x + 3 = 90 \implies 11x - 9 = 90.$$\n\n5. \text{Add } 9 \text{ to both sides: }\n$$11x - \cancel{9} + 9 = 90 + 9 \implies 11x = 99.$$\n\n6. \text{Divide both sides by } 11:\n$$\frac{11x}{\cancel{11}} = \frac{99}{11} \implies x = 9.$$\n\n7. \text{Find } m\angle 2 \text{ by substituting } x=9 \text{ into } m\angle 2 = 8x + 3:\n$$m\angle 2 = 8(9) + 3 = 72 + 3 = 75^\circ.$$\n\n\text{Final answer: } m\angle 2 = 75^\circ.