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Problem Solving:
Mixed Problem Solving
For use with the lesson “Measure and Classify Angles”, “Describe Angle Pair Relationships”, and
“Classify Polygons”
1. Multi-Step Problem The diagram shows
four airport runways and their
intersections.
All runways are straight and MQ bisects
 NTR.
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
a. Which angles are acute? obtuse? right?
b. If m  SVR = 56°, m  NTO = 44°,
and m  QUP = 19°, find m  PVR,
m  OTQ, m  MUS, m  MTO,
m  LTM.
2. Open-Ended The square piece of paper
below has been folded in half three times
and labeled as shown. Name 3 acute
angles,
5 right angles, and 3 congruent obtuse
angles.
3. Gridded Answer The diagram shows a
ramp that is placed between the ground and
a truck bed to load a bicycle. Find
m  MKL
in degrees.
4. Short Response The table shown below
is shaped like a regular pentagon. Use the
diagram to find the length of a side.
Explain.
5. Gridded Answer Suppose that between
sunrise and sunset, the sun travels across
the
sky in a perfect half circle. When the
setting
sun is just 24° above the western horizon,
what is the angle formed by the sun and the
eastern horizon, in degrees?
6. Short Response A roof truss for John’s
house is designed using 6 pieces of wood
that form 4 triangles. The three inner
pieces
are called the truss web. The left and right
pieces of the truss web meet at a right
angle.
The middle piece of the truss web bisects
the straight angle of the bottom chord and
divides the quadrilateral formed into two
congruent triangles. The two pieces that
form the top chord meet at a 120º angle.
a. What are the measures of angles A-F?
b. If the sum of the measures of the
angles of a triangle is 180° what are
the measures of angles G-L?
Answer Key
Lesson 1.6
Problem Solving Workshop: Mixed Problem Solving
1. a. acute: ∠LTM, ∠NTO, ∠OTQ, ∠PUQ, ∠RVS, ∠RTL, ∠NVP, ∠MUS; obtuse:
∠LTN, ∠MTO, ∠OTR, ∠PUM, ∠QUS, ∠RVP, ∠SVN, ∠LTQ; right: ∠MTN, ∠NTQ,
∠QTR, ∠RTM
b. m∠PVR = 124, m∠OTQ = 46, m∠MUS = 19, m∠MTO = 134, m∠LTM = 46
2. Answers will vary.
3. 150
4. 42 in.; 17.5 feet; Sample answer: In a regular pentagon, all sides have equal length.
Because you know the expressions for the length of two sides, set the expressions
equal to each other to find x. Then substitute this value into one of the expressions
to find the length of a side.
5. 156
6. a. m∠A – D = 45, m∠E – F = 60
b. m∠G = 75, m∠H = 105, m∠I + J = 30, m∠K = 105, m∠L = 75