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# Math: Basic Tutorials

## Angle and Triangle Basics

You may be familiar with the phrase ‘do a 180’. It means to turn around and face the opposite direction and comes from the fact that the measure of an angle that makes a straight line has 180 degrees. In this module, we will review the basic properties of angles and triangles and use those properties to solve problems.

## Examples & Activity

### Examples

Click on the titles below to view each example.

### Example 1. An angle measures 13 degrees. Find its complement and supplement.

Line 1: Find the complement. Complementary angles sum to 90 degrees.

Line 2: Let c represent the measure of the complement. Substitute the given values into formula. c plus 13 degrees equals 90 degrees.

Line 3: Solve the equation for the complement. c equals 90 degrees minus 13 degrees, so the complement equals 77 degrees.

Line 4: Find the supplement. Supplementary angles sum to 180 degrees.

Line 5 Let c represent the measure of the supplement. Substitute the given values into formula. s plus 13 degrees equals 180 degrees.

Line 6: Solve the equation for the supplement. s equals 180 degrees minus 13 degrees, so the supplement equals 167 degrees.

Line 7: Answer the question. 77 degrees is the complement of 13 degrees, and 167 degrees is the supplement of 13 degrees.

### Example 2. Find the measure of the missing angle, x. Image text: Triangle ABC is a right-angle triangle. Angle BAC is 90 degrees, angle ABC is 28 degrees, and angle ACB is unknown and labelled x.

Solution:

Line 1: The internal angles of a triangle sum to 180 degrees, so Angle BAC plus angle ABC plus ACB equals 180 degrees.

Line 2: Substitute the given information into the formula. 90 degrees plus 28 degrees plus x equals 180 degrees.

Line 3: Solve the equation for x. 118 degrees plus x equals 180 degrees, so x equals 180 degrees minus 118 degrees, and x is equal to 62 degrees.

Line 4. Answer the question. The measure of the missing angle is 62 degrees.

### Example 4. Triangle ABC and triangle XYZ are similar triangles. Find the length of side y.

Image: Triangle ABC is the larger triangle. The length of side AB is 4, the length of side BC is unknown and labelled as a, and the length of side AC is 3.2. Triangle XYZ is the smaller triangle. The length of side XY is 3, the length of side YZ is 4.5, and the length of side XZ is unknown and labelled as y.

Solution

Line 1. The triangles are similar so the corresponding sides have the same ratio. AB over XY equals BC over YZ equals AC over XZ.

Line 2. Since the side AB corresponds to the side XY we will use this ratio to find the missing side. AB over XY equals 4 over 3.

Line 3. Set up the proportion to find side y. Be careful to match up corresponding sides correctly. AB over XY equals AC over XZ.

Line 4. Substitute the given information into the proportion. 4 over 3 equals 3.2 over y.

Line 5. Solve the equation for y. 4y equals 3 times 3.2, so 4y equals 9.6 and y equals 2.4.

Line 6. Answer the question. Side XZ is 2.4

### Activity

Try this activity to test your skills. If you have trouble, check out the information in the module for help.