Module 5

1. Module 5

1.17. Page 2

Mathematics 10-3 Module 5 Lesson 4

Module 5: Angles

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In this activity you will review several angle relationships that you examined in previous math courses.

Try This

Work with a partner, if possible.

Step 1: On a blank sheet of paper, draw a triangle of any shape and size. Label the angles as shown, and measure the angles with a protractor. Record these measures.

This illustration shows a triangle labelled ABC with the labels A, B, and C inside the corners of the triangle.

Step 2: Cut out the triangle, and then tear off ∠B and ∠C.

Step 3: Place ∠B and ∠C next to ∠A so that all three vertices lie at the same point.

This illustration shows angles torn from the previously described triangle ABC and then fitted together to form a straight line.

Notice that the three angles at A form a straight line. Do you remember that the measure of a straight angle is 180°?

Self-Check

SC 1. Calculate ∠A + ∠B + ∠C. Will this sum be the same for any triangle you draw? Why?

Compare your answer.

Next, you will apply this relationship among the angles of a triangle.

Example 1

This illustration shows triangle ABC, with BC a horizontal line. Angle B is 72 degrees and angle C is 44 degrees.

Find the missing measure of ∠A.

Solution

In a triangle, all the angles add up to 180°, so you know that the following is true: ∠A + ∠B + ∠C = 180°. Use this information to find the value of ∠A.

Then check your answer.

Self-Check

SC 2. Find the missing measure. When finished, check your answer.

This illustration shows triangle PQR. Angle P is 38 degrees and angle R is 33 degrees.

Compare your answer.