Do Now Draw an acute angle and write the measure of the angle in degrees. Draw a right angle and write the measure of the angle in degrees. Draw an obtuse angle and write the measure of the angle in degrees.

Objective TLWBAT calculate unknown angles by using facts about supplementary, complementary, vertical, and adjacent angles to correctly complete at least 8 out of 10 practice problems. NJCCCS A.1 Common Core 7.G.B.5

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Complementary vs. Supplementary Complementary angles When the sum of the measures of two angles is 90°. Supplementary angles When the sum of the measures of two angles is 180°.

Use the diagram to tell whether the angles are complementary, supplementary, or neither. Additional Example 2A: Identifying Complementary and Supplementary Angles OMP and PMQ Since 60° + 30° = 90°, PMQ and OMP are complementary. O N P Q R M To find mPMQ start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° - 75° = 30°. mOMP = 60°.

If the angle you are measuring appears obtuse, then its measure is greater than 90°. If the angle is acute, its measure is less than 90°. Reading Math

Use the diagram to tell whether the angles are complementary, supplementary, or neither. Additional Example 2B: Identifying Complementary and Supplementary Angles NMO and OMR mNMO = 15° and mOMR = 165° O N P Q R M Since 15° + 165° = 180°, NMO and OMR are supplementary. Read mNMO as “the measure of angle NMO.” Reading Math

Use the diagram to tell whether the angles are complementary, supplementary, or neither. Additional Example 2C: Identifying Complementary and Supplementary Angles 8-2 PMQ and QMR O N P Q R M Since 30° + 75° = 105°, PMQ and QMR are neither complementary nor supplementary. To find mPMQ start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° - 75° = 30°. mQMR = 75°.

Use the diagram to tell whether the angles are complementary, supplementary, or neither. Check It Out: Example 2A BAC and CAF mBAC = 35° and mCAF = 145° C B D E F A Since 35° + 145° = 180°, BAC and CAF are supplementary.

Use the diagram to tell whether the angles are complementary, supplementary, or neither. Check It Out: Example 2B CAD and EAF Since 55° + 35° = 90°, CAD and EAF are complementary. C B D E F A To find mCAD start with the measure that DA crosses, 90°, and subtract the measure that CA crosses, 35°. mCAD = 90° - 35° = 55°. mEAF = 35°.

Use the diagram to tell whether the angles are complementary, supplementary, or neither. Check It Out: Example 2C BAC and EAF mBAC = 35° and mEAF = 35° C B D E F A Since 35° + 35° = 70°, BAC and EAF are neither supplementary nor complementary.

Angles A and B are complementary. If mA is 56 °, what is the mB? Additional Example 3: Finding Angle Measures Since A and B are complementary, mA + mB = 90 °. mA + mB = 90 ° 56 ° + mB = 90 ° – 56 ° mB = 34 ° Substitute 56° for mA. Subtract 56° from both sides. The measure of B = 34 °.

Angles P and Q are supplementary. If mP is 32 °, what is the mQ? Check It Out: Example 3 Since P and Q are supplementary, mP + mQ = 180 °. mP + mQ = 180 ° 32 ° + mQ = 180 ° – 32 ° mQ = 148 ° Substitute 32° for mP. Subtract 32° from both sides.. The measure of Q = 148 °.

The symbol means “is parallel to.” The symbol means “is perpendicular to.” Reading Math

Tell whether the lines appear parallel, perpendicular, or skew. Additional Example 1A: Identifying Parallel, Perpendicular, and Skew Lines The lines appear to intersect to form right angles. UV and YV UV  YV 8-3

Tell whether the lines appear parallel, perpendicular, or skew. Additional Example 1B: Identifying Parallel, Perpendicular, and Skew Lines The lines are in different planes and do not intersect. XU and WZ are skew.

Tell whether the lines appear parallel, perpendicular, or skew. Additional Example 1C: Identifying Parallel, Perpendicular, and Skew Lines The lines are in the same plane and do not intersect. XY and WZ XY || WZ

Tell whether the lines appear parallel, perpendicular, or skew. Check It Out: Example 1A The lines appear to intersect to form right angles. WX and XU WX  XU

Tell whether the lines appear parallel, perpendicular, or skew. Check It Out: Example 1B The lines are in different planes and do not intersect. WX and UV are skew.

Tell whether the lines appear parallel, perpendicular, or skew. Check It Out: Example 1C The lines are in the same plane and do not intersect. WX and ZY WX || ZY

Adjacent angles have a common vertex and a common side, but no common interior points. Angles 2 and 3 in the diagram are adjacent. Adjacent angles formed by two intersecting lines are supplementary Vertical angles are the opposite angles formed by two intersecting lines. Angles 1 and 3 in the diagram are vertical angles. Vertical angles have the same measure, so they are congruent.

Angles with the same number of tick marks are congruent. The tick marks are placed in the arcs drawn inside the angles. Reading Math

A transversal is a line that intersects two or more lines. Transversals to parallel lines form special angle pairs.

Line n line p. Find the measure of the angle. Additional Example 2A: Using Angle Relationships to Find Angle Measures 22 2 and the 130° angle are vertical angles. Since vertical angles are congruent, m2 = 130°.

Line n line p. Find the measure of the angle. Additional Example 2B: Using Angle Relationships to Find Angle Measures 33 m ° = 180° –130° m  3 = 50° Adjacent angles formed by two intersecting lines are supplementary. Subtract 130° to isolate m3.

Line n line p. Find the measure of the angle. Additional Example 2C: Using Angle Relationships to Find Angle Measures 44 Alternate interior angles are congruent. m4 = 130°.

Line n line p. Find the measure of the angle. Check It Out: Example 2A 33 3 and the 45° angle are vertical angles. Since vertical angles are congruent, m3 = 45°. 45° ° np

Line n line p. Find the measure of the angle. Check It Out: Example 2B 66 6 and the 135° angle are vertical angles. m6 = 135°. 45° ° np

Line n line p. Find the measure of the angle. Check It Out: Example 2C 44 m4 + 45° = 180° –45° m  4 = 135° Adjacent angles formed by two intersecting lines are supplementary. Subtract 45° to isolate m4. 45° ° np

Closure What are the 3 special relationships between angles one can find from parallel lines with a transversal?

Complementary Angles Problem 1 What is the measure of ∠ a below? Problem 2 What is the measure of ∠ a below? Problem 3 If the ratio of two complementary angles is 2:1, what is the measure of the smaller angle? (Hint 2x + 1x = 90)

Supplementary Angles Problem 1 If m ∠ 1=32 degrees, what is the m ∠ 2? Problem 2 ∠ C and ∠ F are supplementary. If m ∠ C is 25 degrees, what is the m ∠ F ? Problem 3If the ratio of two supplementary angles is 2:1, what is the measure of the larger angle? (Hint 2x + 1x = 180)

Vertical and Adjacent Angles Problem 1 (Vertical)Find ∠ a° if ∠ b is 62° Problem 2 (Adjacent) Find ∠ 3° Problem 3 (Both)Find angles a°, b° and c° below

Corresponding Angles Problem 1 (complementary) If ∠ a is 77°, what is ∠ b °? Problem 2 What is ∠ f °? Problem 3 What is ∠ e°?