8-3 Angle Relationships Warm Up Problem of the Day Lesson Presentation Course 1 Warm Up Problem of the Day Lesson Presentation

Warm Up Identify the type of angle. 1. 70° 2. 90° 3. 140° 4. 180° acute right obtuse straight

Problem of the Day A line forms an angle of 57° with the vertical axis. What angle does the line form with the horizontal axis? 33° or 147°

Learn to understand relationships of angles.

Vocabulary congruent vertical angles adjacent angles complementary angles supplementary angles

When angles have the same measure, they are said to be congruent. Vertical angles are formed opposite each other when two lines intersect. Vertical angles have the same measure, so they are always congruent. MRP and NRQ are vertical angles. MRN and PRQ are vertical angles

Adjacent angles are side by side and have a common vertex and ray Adjacent angles are side by side and have a common vertex and ray. Adjacent angles may or may not be congruent. MRN and NRQ are adjacent angles. They share vertex R and RN. NRQ and QRP are adjacent angles. They share vertex R and RQ.

Additional Example 1A: Identifying Types of Angle Pairs Identify the type of each angle pair shown. 5 6 5 and 6 are opposite each other and are formed by two intersecting lines. They are vertical angles.

Additional Example 1B: Identifying Types of Angle Pairs Identify the type of each angle pair shown. 7 and 8 are side by side and have a common vertex and ray. 7 8 They are adjacent angles.

Identify the type of each angle pair shown. Check It Out: Example 1A Identify the type of each angle pair shown. 3 and 4 are side by side and have a common vertex and ray. 3 4 They are adjacent angles.

Identify the type of each angle pair shown. Check It Out: Example 1B Identify the type of each angle pair shown. 7 8 7 and 8 are opposite each other and are formed by two intersecting lines. They are vertical angles.

Complementary angles are two angles whose measures have a sum of 90°. 65° + 25° = 90° LMN and NMP are complementary. P N M L 25° 65°

Supplementary angles are two angles whose measures have a sum of 180°. 65° + 115° = 180° GHK and KHJ are supplementary. J K H 115° 65° G

Additional Example 2A: Identifying an Unknown Angle Measure Find each unknown angle measure. The angles are complementary. The sum of the measures is 90°. 71° + 1 = 90° 1 –71° –71° m1 = 19° 71°

Additional Example 2B: Identifying an Unknown Angle Measure Find each unknown angle measure. The angles are supplementary. The sum of the measures is 180°. 125° + 2 = 180° –125° –125° m2 = 55° 125° 2

Additional Example 2C: Identifying an Unknown Angle Measure Find each unknown angle measure. The angles are vertical angles. 3 82° m3 = 82° Vertical angles are congruent.

Additional Example 2D: Identifying an Unknown Angle Measure Find each unknown angle measure. x 80° K M L N J y JKL and MKN are congruent. x + y + 80° = 180° The sum of the measures is 180°. –80° –80° x + y = 100° Each angle measures half of 100°. x = 50° and y = 50°

Check It Out: Example 2A Find each unknown angle measure. The angles are complementary. 65° + d = 90° The sum of the measures is 90°. d –65° –65° md = 25° 65°

Check It Out: Example 2B Find each unknown angle measure. The angles are supplementary. 145° + s = 180° The sum of the measures is 180°. –145° –145° ms = 35° 145° s

Find each unknown angle measure. Check It Out: Example 2C Find each unknown angle measure. The angles are vertical angles. t mt = 32° Vertical angles are congruent. 32°

Check It Out: Example 2D Find each unknown angle measure. x 50° B D C E A y ABC and DBE are congruent. x + y + 50° = 180° The sum of the measures is 180°. –50° –50° x + y = 130° Each angle measures half of 130°. x = 65° and y = 65°

Lesson Quiz 1. Identify the type of angle pair shown. Find each unknown angle measure. 2. The angles are vertical angles. 3. The angles are supplementary. 6 7 adjacent d d = 130° 130° x = 45° x 135°