MATHEMATICS · Multi-part · AoPS · Mathematics · One-Variable Linear Equations · One-Variable Linear Equations
Problem
Let two angles be (7k−4)∘ and (2k+49)∘, where k is a real number. Answer the following questions.
(i) Form the equation that must hold if the two angles are complementary.
(ii) Solve the equation obtained in part (i) to find all real values of k that satisfy the condition.
(iii) Prove that there is exactly one integer value of k that satisfies the equation from part (ii).
(iv) For that integer value of k, determine the measures of the two angles and classify each as acute, right, or obtuse, giving reasons.
(v) Verify that the angles calculated in part (iv) are indeed complementary.