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Measuring Angles Chapter 1 Section 4 Common Core Standard: G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc. Vocabulary Angle: Formed by 2 rays with the same endpoint. Sides: The rays of an angle. Vertex: The endpoint of an angle. Naming angles: there are 3 ways By the letter at the vertex. A letter on each side and the vertex. Vertex letter is the middle letter. By a number inside the angle. A B 1 C Vocabulary The interior of an angle is the region between the two sides. The exterior of an angle is the region outside of the two sides. A B 1 C Vocabulary Acute angle: measures between 0 and 90 degrees Right Angles: Measures exactly 90 degrees Obtuse angle: Measures between 90 and 180 degrees Straight angle: Measures exactly 180 degrees Made of two opposite rays. Congruent Angles: Angles with the same measure Protractor Postulate (1-7) This postulate allows you to measure an angle using a protractor. The measure of an angle is the absolute value of the difference of the real numbers paired with the two rays. IE: Take the number for each ray – subtract them – find the absolute value. Example 1 What is the measure of angle BOC? _____________ What is the measure of angle BOD? _____________ What is the measure of angle COA? _____________ What is the measure of angle DOC? _____________ Angle Addition Postulate (1-8) If point b is in the interior of AOC, then m AOB + m BOC = m AOC Meaning: If you have two adjacent angles you can add the measure of the two angles to find the measure of the large angle. A B O C Example 2 A 4x - 20 If m AOC = 155, find m AOB and m B 3x + 14 O C BOC Checkpoint Turn to page 31. With a partner – answer questions 1 – 5. You will have 8 minutes to complete this before we go over. Homework Pg 31# 6 – 20 even, 22, 23, 28, 29, 30, 42, 43