Chapter 5 Quiz
Study Guide
Scheduled for Wednesday February 11th
- Lines (Lesson 1)
4)
- Angles of Triangles (Lesson 3)
- Polygons & Angles (Lesson
Lesson 1 - Lines
In the figure above, lines m and n are parallel to one another and are intersecting
by a line called a “Transversal.” When this happens, special angles are made.
Adjacent Angles-Angles that are NEXT TO each other. They share a
common side. These angles are SUPPLEMENTARY which means the sum of
these two angles is equal to 180 DEGREES.
Adjacent angles: < 1 & < 2
<3 &<4
<5 &<6 <7 &<8
<1 &<3
<2 &<4
<5 &<7 <6 &<8
Vertical Angles- Angles that are OPPOSITE from each other. They share a
common vertex. These angles are CONGRUENT which means they are equal in
measure.
Vertical angles: < 1 & < 4
<2 &<3
<5 &<8 <6 &<7
Corresponding Angles-When two parallel lines are crossed by another
line (which is called the Transversal), the angles in matching corners are called
corresponding angles. These angles are CONGRUENT. (“same spot different
group”)
Corresponding Angles: < 1 & < 5
<2 &<6
<3 &<7 <4 &<8
Alternate Interior Angles-When two parallel lines are crossed by
another line (which is called the Transversal), the pairs of angles on opposite
sides of the transversal but inside the two lines are called Alternate Interior
Angles. These angles are CONGRUENT. (“inside the walls of the parallel lines”)
Alternate Interior Angles: < 3 & < 6
<4 &<5
Alternate Exterior Angles-When two parallel lines are crossed by
another line (which is called the Transversal), the pairs of angles on opposite
sides of the transversal but outside the two lines are called Alternate Exterior
Angles. These angles are CONGRUENT. (“outside the walls of the parallel
lines”)
Alternate Exterior Angles: < 1 & < 8
<2 &<7
Finding Missing Angles
Suppose you know that m<1 = 50° You can use that information to figure out the
measures of angles 2, 3, and 4.
YOU MUST JUSTIFY USING VOCABULARY TERMS!!
(vertical, supplementary, corresponding, alt. interior, alt. exterior)
Lesson 3 – Angles of Triangles
All Triangles are 180°
Finding Interior Angles of Triangles
Find the value of c in the given triangle
38 + 85 + c = 180
123 + c = 180
C = 57°
The missing angle is 57°.
Find the value of x in the given triangle
45°, 65°
1  Add the two angles given 45 + 65 = 110
nd
2  Subtract the sum from 180 (180° in total triangle) 180-110 =70
The missing angle is 70°.
st
Ratio Interior Angles of Triangles
The angles in triangle ABC are in the ratio 2: 3: 4. What are the measures of these
angles?
2x + 3x + 4x = 180°
9x = 180  combine like terms
x = 20°  solve for x
NOT DONE YET!! 2(20) = 40° 3(20) = 60° 4(20) = 80°
Finding Exterior Angles of Triangles
interior angle + interior angle = exterior angle
The two “interior angles” are x° and 22°. The “exterior angle” is 134°.
x + 22 = 134 (interior + interior = exterior)
x = 112°
The two “interior angles” are x° and 58°. The “exterior angle” is 120°.
x + 58 = 120 (interior + interior = exterior)
x = 62°
Lesson 4 – Polygons and Angles
The formula to find interior angles of a polygon is (n – 2 )180°
Where “n” = the number of sides in the polygon.
In a REGULAR POLYGON  all sides and angles are equal
Finding Interior Angles of Polygons
 Find the sum of the interior angles in an octagon.
An octagon has 8 SIDES so n=8
(8 – 2)180
(6)180
1,080 The sum of the interior angles is 1,080°. (this is ALL of the angles
put together)
 Find the measure of one interior angle in an 19-agon.
A nineteen has 19 SIDES so n= 19
(19 – 2)180
(17)180
3,060 The sum of the interior angles is 3,060°. (this is ALL of the angles
put together)
NOT DONE YET!! Need to find ONE interior angle, not the sum of them all
3060 ÷ 19 = 161.1°
One interior angle is 161.1°
Finding Exterior Angles of Polygons
No matter how many sides in a polygon, the SUM of all the EXTERIOR
ANGLES =
360°
 Find the measure of an exterior angle in a regular decagon.
There are 10 sides in a decagon.
So to find the measure of each exterior angle….
10x = 360
x = 36°
 Find the measure of an exterior angle in a regular hexagon.
There are 6 sides in a hexagon.
So to find the measure of each exterior angle….
6x = 360
x = 60°
Practice for the Quiz
Textbook “Got It” problems from Lessons 1, 3, and 4
“Got It” problems on page 373
See Ms. Molinari or Mrs. Labato before/after school for extra help and review.
Good Luck!