Six times the complement of an angle is 12° less than twice its supplement. Find the measure of the angle.

Introduction / Context:Complementary angles sum to 90°, and supplementary angles sum to 180°. The statement links linear expressions of the same unknown through these definitions.

Given Data / Assumptions:

• Angle = x°.
• Complement = 90 − x; supplement = 180 − x.
• Condition: 6(90 − x) = 2(180 − x) − 12.

Concept / Approach:Translate to an equation in x and solve. Keep complements and supplements distinct.

Step-by-Step Solution:

Verification / Alternative check:Complement = 42°, supplement = 132°. LHS = 6*42 = 252; RHS = 2*132 − 12 = 264 − 12 = 252 ✓.

Why Other Options Are Wrong:They fail the given linear relation when checked.

Common Pitfalls:Mixing up 90 − x and 180 − x; arithmetic slips while simplifying; sign mistakes with the “12° less”.

Final Answer:48°