CHAPTER 10 / ESSENTIAL GEOMETRY SKILLS 363
Concept Review 1
- Only cand eare congruent.
2.a+b+c= 180 °, c+d= 180 °, d+e= 180 °,
e+a+b= 180 °
3.∠ 5
4.∠7 and ∠ 13
5.∠12 and ∠ 14
6.∠ 4
7.∠11, ∠8, and ∠ 6
Answer Key 1: Lines and Angles
- equal
- supplementary
- neither
- supplementary
- neither
- supplementary
- supplementary
- C Notice that the m°angle has a “corresponding”
angle below that has the same measure. (Notice
that they form an F.) Then (m+5) +n+m=180.
Simplify: 2 m+ 5 +n= 180
Subtract (5 + 2 m): n= 175 − 2 m- C Draw an extra line through the vertex of the
angle that is parallel to the other two. Notice that
this forms two “Z” pairs. Therefore, x= 36 + 43 =79.
43 °
36 °
1
2
43 °
36 °m°m+ 5 °
n° 12
m°SAT Practice 1
- C Draw in the three angles that are “vertical,”
and therefore congruent, to the angles that are
shown. Then choose any three adjacent angles,
and notice that they form a straight angle. There-
fore, x+ 2 x+ 3 x=180. So 6x=180 and x=30. - B The opposite angles in a parallelogram must be
equal, and any two “consecutive angles” as you
move around the figure must be supplementary.
(Notice that consecutive angles form C’s or U’s. If
you’re not sure why this theorem is true, sketch a
few sample parallelograms and work out the angles.)
The angle opposite the y°must also measure y°, and
when this is added to the three z°angles, they form
a straight angle. Therefore, y+ 40 + 40 + 40 = 180
and y=60. - E In the triangle, the angles must have a sum of
180 °. (See the next lesson for a simple proof.)
Therefore, the other two angles in the triangle
must have a sum of 50°. Pick values for these two
angles that add up to 50°, and write them in. It
doesn’t matter how you do it: 25°and 25°, 20°and
30 °, 40°and 10°, as long as they add up to 50°. You
can then find the values of aand bby noticing that
they form straight angles with the interior angles.
So if the interior angles are 25°and 25°, then aand
bmust both be 155.