Chapter Review
1. Determine the measure of the unknown angle.
a)
76° + ZA
ZA
ZA
b)
E
r\°
180°
180°
180°-76°
104°
43° + 74° + ZD
180°
117° +ZD
180°
+ 40° + ZA
ZD
180°-117C
ZD
63°
ZD= 63°
2. Can a triangle have 2 interior angles that are obtuse? Justify your answer.
No. The sum of all 3 interior angles of any triangle is exactly 180°. An obtuse
angle is greater than 90°, so the sum of 2 obtuse angles is greater than 180°.
3.2 3. Determine the measure of the exterior angle.
b)
a)
ZGJK = 51°
ZGJK= 92°
ZLNP = 37° + 105°
ZLNP = 142°
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3.3 4. A train travels in a straight line on a bridge over a river.
The river runs between 2 parallel roads.
Determine the measures of angles s and t.
t and 88° are interior angles.
So, f + 8 8 ° = 180°
t - 180° -88°
t - 92°
s and fare opposite angles.
f = 9 2 ° , s o s = 92°
= 92°
= 92°
5. Determine the unknown angles.
Label each angle relationship as corresponding, alternate, or interior.
c)
b)
a)
x = 56°
These are alternate
angles.
= 180° -76° = 104°
These are interior
v
angles.
• = 66°
These are corresponding
angles.
6. A transversal forms a 53° angle with one line
and a 137° angle with a second line as shown.
Are the two lines parallel?
Justify your answer.
No. Sample Answer: The angle marked 53° is equal to the angle opposite it. This
angle and the angle marked 137° are interior angles. Their sum is: 53° + 137° =
190°. The sum of interior angles between parallel lines is 180°. so the two lines
are not parallel.
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3.4 7. A robot is programmed to move forward 3 m and turn right 75°.
It repeats this instruction 4 times.
a) Will the robot begin and end at the same place? Justify your answer.
No. If the robot begins and ends at the same place, its path will form a
quadrilateral. The sum of the interior angles in a quadrilateral is 360°, but
4 x 75° = 300°, so the robot will not begin and end at the same place.
b) How could you change the instructions so the path of the robot forms a quadrilateral?
The robot's program must tell it to turn right 90° each time.
8. Determine the measure of the unknown angles in the parallelogram.
y and 70° are the measures of interior angles between parallel sides AB and CD.
So, y + 7 0 ° = 180°
y = 180°-70°
y = 110°
z and y are the measures of interior angles between parallel sides AD and BC.
So, z + y= 180°
Substitute:/=110°
z = 180°-110°
z = 70°
y= 110° and z = 70°
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9. A stop sign is a regular polygon with 8 sides.
What is the measure of each interior angle?
S = (n-2)x180°
Substitute: n = 8
S = (8-2)x180°
= 6x180°
= 1080°
Since the angles are equal, divide by 9 to determine the measure of each angle.
loso: = 1350
8
Each interior angle is 135° .
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10. Determine the angle measure indicated by x.
a)
S = (n-2)x180°
Substitute: n - 5
S=(5-2)x180°
= 3x180°
= 540°
The sum of the interior angles is 540°.
Another way to write the sum of the
interior angles is:
x + 100° + 97° + 85° + 140° = x + 422°
So, x + 422° = 540°
x = 540° - 422°
x = 118°
x= 118°
b)
S = (n-2)x180°
Substitute: n = 4
S=(4-2)x180°
= 2x180°
= 360°
The sum of the interior angles is 360°.
Another way to write the sum of the
interior angles is:
x + 30° + 42° + 270° = x + 342°
So, x + 342° = 360°
x= 360°-342°
x=18°
x= 18°
11.Compare the 2 polygons.
Is the sum of the exterior angles
for the hexagon greater than the
sum of exterior angles for the
pentagon? Justify your answer.
No. The sum of the exterior angles of any polygon is 360°. So, the sum of the
exterior angles of a pentagon and a hexagon are the same.
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