Two angles measure (5y + 62°) and (22° + y). If the two angles are supplementary (their sum is 180°), find the value of y in degrees.

Introduction / Context: This question checks a basic geometry fact: supplementary angles add up to 180°. Once you translate the statement into an equation, it becomes a simple linear equation in y.

Given Data / Assumptions:

• Angle 1 = (5y + 62°) • Angle 2 = (22° + y) • Supplementary means: Angle 1 + Angle 2 = 180° • Required: y (in degrees)

Concept / Approach: Use the definition of supplementary angles: (5y + 62) + (22 + y) = 180. Combine like terms (y terms together and constants together), then isolate y by basic algebra.

Step-by-Step Solution: 1) Form the equation from supplementary condition: (5y + 62) + (22 + y) = 180 2) Combine y terms: 5y + y = 6y 3) Combine constants: 62 + 22 = 84 4) So the equation becomes: 6y + 84 = 180 5) Subtract 84 from both sides: 6y = 96 6) Divide both sides by 6: y = 16 7) Therefore y = 16°.

Verification / Alternative check: Substitute y = 16: Angle 1 = 5*16 + 62 = 80 + 62 = 142°. Angle 2 = 22 + 16 = 38°. Sum = 142° + 38° = 180°, so the condition holds exactly.

Why Other Options Are Wrong: • 32°, 24°, 8°, 1°: substituting any of these values does not make the two expressions add to 180°.

Common Pitfalls: • Treating supplementary as “equal” instead of “sum to 180°”. • Forgetting to combine y terms correctly (5y + y = 6y).

Final Answer: 16°