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Geometry 1.3 Angles and Their Measures Name ______________________________ Date ________________ Period ______ Objectives Name and classify angles. Measure and construct angles and angle bisectors. angle – a figure formed by two ______, or sides, with a common _____________ called the vertex (plural: vertices). Angle Name: ________, ________, ________, or _______ You cannot name an ______ just by its ______ if the point is the vertex of more than ____ _______. In this case, you must use all _____ _______ to name the angle, and the _______ point is always the vertex. Example 1 Write the different ways you can name the angles in the diagram. Example 2 Classify each angle as acute, right, or obtuse. A. XTS B. WTU C. XTU Example 3 Find the measure of each angle. Example 4 Use a protractor to draw an angle with a measure of 165°. Example 5 Find the measure of each angle. Then classify each as acute, right, or obtuse. A. YXW B. ZXW C. WXV Example 6 Find the measure of each angle. Then classify each as acute, right, or obtuse. A. AOB B. BOC C. COD D. DOB Congruent angles are angles that have the same ___________. In the diagram, mABC = mDEF, so ABC DEF. Example 7 Example 8 mDEG = 115°, and mDEF = 48°. Find mFEG. K is in the interior of LMN, mLMK =52°, and mKMN = 12°. Draw the picture. Find mLMN. An angle bisector is a _____ that divides an angle into ____ _________ ______. ⃗⃗⃗⃗ bisects LJM; JK thus LJK KJM. Example 9 ⃗⃗⃗⃗⃗⃗ bisects JKL, mJKM = (4x + 6)°, and KM mMKL = (7x – 12)°. Find mJKM. Example 10 ⃗⃗⃗⃗ bisects LJM, mLJK = (-10x + 3)°, and JK mKJM = (–x + 21)°. Find mLJM. Example 11 ⃗⃗⃗⃗⃗ QS bisects PQR, mPQS = (5y – 1)°, and mPQR = (8y + 12)°. Find mPQS. Example 12 1 ⃗⃗⃗⃗⃗ BD bisects ABC, mABD = (2y + 10) °, and mDBC = (y + 4)°. Find mABC.