Geo 1.5 Angle Relationships
Name __________________________________
Learning Objective: After this lesson, you should be able to successfully solve multi-step problems using
angle relationships.
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.
G.MG.1 Use geometric shapes, their measures, and their properties to describe objects.
For Exercises 1-6, use the figure at the right. Name an angle or angle pair that satisfies each condition.
1. Name two acute vertical angles.
2. Name a linear pair.
3. Name two obtuse vertical angles.
4. Name two acute adjacent angles.
5. Name an angle complementary to FKG.
6. Name an angle supplementary to FKG.
7. Find the measures of an angle and its complement if one angle measures
24 degrees more than the other.
8. The measure of the supplement of an angle is 36 less than the measure of
the angle. Find the measures of the angles.
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9. If mRTS = 8x + 18, find the value of x so that TR ⊥ TS .
10. If mPTQ = 3y − 10 and mQTR = y, find the value of y so that PTR is a right angle.
Determine whether each statement can be assumed from the figure. Explain.
11. WZU is a right angle.
12. YZU and UZV are supplementary.
13. VZU is adjacent to YZX.
14. Two angles are complementary. The measure of one angle is 21 more than twice the measure of the other
angle. Find the measures of the angles.
15. If a supplement of an angle has a measure 78 less than the measure of the angle, what are the measures
of the angles?
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16. If mFGE = 5x + 10, find the value of x so that FC  AE .
17. If mBGC = 16x − 4 and mCGD = 2x + 13, find the value of x
so that BGD is a right angle.
18. A rectangular plaza has a walking path along its perimeter in addition to two paths that cut across the plaza
as shown in the figure.
a) Find the measure of 1.
b) Find the measure of 4.
c) Name a pair of vertical angles in the figure.
d) What is the measure of 2?