Nick has a slice of cake. He wants to cut it in half, bisecting the 46° angle formed by the straight edges of the slice. What will be the measure of the angle of each of the resulting pieces? What would the angle measures be if he bisected those two pieces, creating four slices of cake? Problem of the Day

Section 1-5 Angle Relationships

Then Now Objectives You measured and classified angles. Identify and use special pairs of angles. Identify perpendicular lines.

Common Core State Standards Content Standards Mathematical Practices Common Core State Standards Preparation for G.SRT.7 – Explain and use the relationship between the sine and cosine of complementary angles. 2) Reason abstractly and quantitatively. 3) Construct viable arguments and critique the reasoning of others.

Special Angle Pairs

Name a pair of adjacent ∠s. Name a linear pair Name a pair of adjacent ∠s. Name a linear pair. Name a pair of vertical ∠s. Example 1

Angle Pair Relationships

Find the measures of two complementary angles if the measure of the larger angle is 12 more than twice the measure of the smaller angle. Example 2

Find the measures of two supplementary angles if the measure of one angle is 6 less than five times the measure of the other angle. Example 2

The measures of two complementary angles are 7x + 17 and 3x – 20 The measures of two complementary angles are 7x + 17 and 3x – 20. Find the measure of the angles. Example 2

Perpendicular: lines, segments, or rays that form right angles. Vocabulary

Perpendicular Lines

Suppose m∠IHS = 3x – 12. Find x so that 𝐻𝐼 and 𝐻𝑆 are perpendicular. Example 3

Lines x and y intersect to form adjacent angles 2 and 3 Lines x and y intersect to form adjacent angles 2 and 3. If m∠2 = 3a – 27 and m∠3 = 2b + 14, find the values of a and b so that x is perpendicular to y. Example 3

Interpreting Diagrams

Determine whether each statement can be assumed from the figure Determine whether each statement can be assumed from the figure. Explain. ∠CAD and ∠DAB are complementary. ∠EDB and ∠BDA are adjacent angles. Example 4

Determine whether each statement can be assumed from the figure Determine whether each statement can be assumed from the figure. Explain. ∠GHL and ∠LHJ are supplementary. ∠GHM and ∠MHK are adjacent angles. Example 4

p.51 #19 – 25 odd, 28, 29, 31, 33 – 35, 45 Homework