Review of Angles

This page has a review of the trigonometric concepts relating to angles for the ACT math examination.

Attempt the problem below and then study the solution.

∠A and ∠B each have measurements between 0° and 45°.

If cos A = sin B, what is the sum of ∠A + ∠B ?

A. 15

B. 30

C. 45

D. 90

E. 180

The correct answer is D.

Remember these important trigonometric formulas:

cos A = sin (90° − A)

sin A = cos (90° − A)

If sin B = cos A, as in this problem, then B = 90° − A

So A + B = A + (90° − A)

A + B = A + 90° − A

A + B = A − A + 90°

A + B = 90°

Review of Angle Laws

You should also review the following angle laws  for your exam.

  1. Two angles are supplementary if they add up to 180 degrees. This means that when the two are placed together, they will form a straight line on one side.
  2. Two angles are complementary (sometimes called adjacent angles) if they add up to 90 degrees. This means that they will form a right triangle.
  3. When two parallel lines are cut by a transversal (a straight line that runs through both of the parallel lines), 4 pairs of opposite (non-adjacent) angles are formed and 4 pairs of corresponding angles are formed. The opposite angles will be equal in measure, and the corresponding angles will also be equal in measure.
  4. A parallelogram is a four-sided figure in which opposite sides are parallel and equal in length. Each angle will have the same measurement as the angle opposite to it.

Go back to the Trigonometry Problems Page.

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