Download Measuring and Constructing Angles

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.
mGEF is ____.
mDEG 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.mCFB if AFC is a straight angle.
________________________________________
11. mEFC if DFC  AFB.
________________________________________
10. mEFA if the angle is congruent to DFE.
________________________________________
12. mCFG 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