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Name: _______________________________ Date: ___________________ Measuring and Constructing Angles An ________________ is a figure made up of two ___________, or sides, that have a common endpoint. The endpoint is called the ____________ of the angle. There are four ways to name this angle: ________________ ________________ ________________ ________________ Name each angle in three ways. 1. 2. ________________________________________ ________________________________________ 3. Name three different angles in the figure. ________________________________________ Angle Acute Right Picture Possible Measures Classify each angle as acute, right, obtuse, or straight. 4. NMP _________________ 5. QMN _________________ 6. PMQ _________________ Obtuse Straight You can use a protractor to find the measure of an angle. mGEF is ____. mDEG is ____. Example: If point W is in the interior of XVU, find the measure of XVU. Angles are ________________ if their measures are equal. In the figure above, XVW WVU because the angles have equal measures. VW is an _______________ _________________ of XVU because it divides XVU into two congruent angles. Find each angle measure. 9.mCFB if AFC is a straight angle. ________________________________________ 11. mEFC if DFC AFB. ________________________________________ 10. mEFA if the angle is congruent to DFE. ________________________________________ 12. mCFG if FG is an angle bisector of CFB. ________________________________________ Copying an Angle with a Compass and Straightedge Steps 1. Use a straightedge to draw a ray with endpoint D. 2. Place the compass on point A and draw an arc that intersects both sides. Label the intersections points B and C. 3. Using the same compass setting, place compass on point D and draw an arc that intersects the ray. Label the intersection point E. 4. Place the compass on point B and open the compass to the distance of BC. 5. Place compass on point E and draw an arc. Label intersection point with first arc F. 6. Use a straightedge to draw ⃗⃗⃗⃗⃗ 𝐷𝐹 . Use the instructions above to copy angle A. A Copy each of the angles below. 1. 2. A A Constructing an Angle Bisector with a Compass and Straightedge Steps 1. Place the compass on point A and draw an arc that intersects both sides. Label the intersections points B and C. 2. Without changing the compass setting, draw intersecting arcs from points B and C. Label the intersection of the arcs D. 3. Use a straightedge to draw ⃗⃗⃗⃗⃗ 𝐴𝐷. Use the instructions above to bisect angle A. A Draw the angle bisector of each angle below. 1. 2. A A ⃗⃗⃗⃗⃗⃗ bisects ∠ABC, m∠ABD = (6x + 3)°, and m∠DBC = (8x – 7)° . Find m∠ABD. Example: If 𝐵𝐷 Your turn. 1. If ⃗⃗⃗⃗⃗ 𝑄𝑆 bisects ∠PQR, m∠PQS = (5y – 1)°, and m∠𝑃𝑄𝑅 = (8y + 12)° . Find m∠PQS. ⃗⃗⃗⃗ bisects ∠LJM, m∠LJK = (-10x + 3)°, and m∠KJM = (-x + 21)° . Find m∠𝐿𝐽𝑀. 2. If 𝐽𝐾