### 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.

- 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.
- Two angles are complementary (sometimes called adjacent angles) if they add up to 90 degrees. This means that they will form a right triangle.
- 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.
- 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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