Author: Kathy Halverson
Last saved by: Glencoe Mathematics
Company: Halverson Household

Lesson 9-3

Example 1	Find Angle Measures
Find the value of x in  ΔABC.

m∠A + m∠B + m∠C = 180		The sum of the measures is 180.
               x + 54 + 62 = 180		Replace m∠B with 54 and m∠C with 62.
                     x + 116 = 180		Simplify.
           x + 116 – 116 = 180 – 116	Subtract 116 from each side.
	       x = 64		Simplify.

The measure of ∠A is 64°

Example 2	Use Ratios to Find Angle Measures
ALGEBRA	The measures of the angles of a certain triangle are in the ratio 1:3:5.
What are the measures of the angles?

Words	The sum of the measures is 180.

Variables	Let x represent the measure of the first angle, 3x the measure of the second angle, and 5x the measure of the third angle.

Equation	x + 3x + 5x = 180		The sum of the measures is 180.
		  9x = 180		Combine like terms.
		  = 		Divide each side by 9.
		    x = 20		Simplify.

	Since x = 20, 3x = 3(20) or 60, and 5x = 5(20) or 100.  The measures of the angles are 20°, 60°, and 100°.

Example 3	Classify Angles
Classify each angle as acute, obtuse, right, or straight.
a. 			b.  				c.  

     m∠ABC < 90°.		     m∠DEF > 90°.		     m∠GHI = 90°.
     So, ∠ABC is acute.		     So, ∠DEF is obtuse.	     So, ∠GHI is right.

Example 4	Classify Triangles
Classify the triangle by its angles and by its sides.

Angles	ΔABC	has one obtuse angle.
Sides	ΔABC has no two sides that are congruent.  

So, it is an obtuse scalene triangle.