Section 1 4 Measure Classify Angles o An

Section 1. 4 Measure & Classify Angles o An angle consists of 2 different rays with the same endpoint. o are the sides. B o A is called the vertex. o We name the angle as: A C

Naming an angle. o E is the vertex. o The sides are Interior o Name the angle: 1 Exterior q A protractor is used to measure an angle in degrees.

EXAMPLE Name angles Name three angles in the diagram. WXY, or YXW YXZ, or ZXY WXZ, or ZXW You should not name any of these angles X because all three angles have X as their vertex.

Classifying Angles o Right angle = 90˚ o Acute angle < 90˚ o Obtuse angle > 90˚but <180˚ o Line = 180˚ o Straight angle = 180˚

EXAMPLE Measure and classify angles Use the diagram to find the measure of the indicated angle. Then classify the angle. a. KHJ b. GHK c. SOLUTION A protractor has an inner and an outer scale. When you measure an angle, check to see which scale to use. GHJ d. GHL

EXAMPLE a. b. c. Measure and classify angles HJ is lined up with the 0 o on the inner scale of the o protractor. HK passes through 55 on the inner o scale. So, m KHJ = 55. It is an acute angle. o HG is lined up with the 0 on the outer scale and o HK passes through 125 on the outer scale. So, o m GHK = 125. It is an obtuse angle. m GHJ = 180. o It is a straight angle. o d. m GHL= 90. It is a right angle.

Angle Addition Postulate 1 2

Angle Addition Postulate 65˚ 3 x + 5 + 2 x + 4 = 84 5 x + 9 = 84 -9 5 x 5 x -9 = 75 5 = 15 40˚

PRACTICE 3. Given that and m HFG. EFG is a right angle, find m ANSWER 60°, 30° EFH

PRACTICE Find the indicated angle measures. 4. Given that KLM is a straight angle, find m and m NLM. ANSWER 125°, 55° KLN

Angle Bisector o A line, ray or segment that divides an angle into two congruent/equal angles.

5 x – 18 = 3 x + 8 -3 x 2 x – 18 = + 18 8 +18 2 x = 26 2 2 x = 13

Constructions o Construct an angle congruent to a given angle. o Construct an angle bisector