Victory for the ACT Student Text 15e

236 • M ATH

LESSON 4 Geometry LINES AND ANGLES

 –Š‡ ϐ‹‰—”‡ „‡Ž‘™ǡ x

?

 –Š‡ ϐ‹‰—”‡ „‡Ž‘™ǡ l Which of the following must

1 is parallel to l be true?

2 .

1.

3.

Throwback to Math Class 1. The degree measure of a straight angle is 180°. 2. The degree measure of a right angle is 90°. 3. The total number of degrees in a circle is 360°. Throwback to Math Class The big angle/ little angle theorem comes in handy: When two parallel lines are intersected by a third line, the following are true: (1) all of the big angles are equal; (2) all of the little angles are equal; and (3) the degree measure of any big angle plus any little angle equals 180°.

A. 45 B. 60 C. 75 D. 90 E. 120

I. w a II. y b 180 + = III. x d 180 + = A. I only B. II only C. I and II only D. II and III only E. I, II, and III  –Š‡ ϐ‹‰—”‡ „‡Ž‘™ǡ x

 –Š‡ ϐ‹‰—”‡ „‡Ž‘™ǡ x

=?

2.

?

F. 45 G. 60 H. 90 J. 105 K. 120

4.

F. 30 G. 45 H. 60 J. 75 K. 90

Throwback to Math Class Remember the following facts about triangles: 1. The sum of the interior angles of a triangle is 180°. 2. An equilateral triangle (three equal sides) has three 60° angles. Therefore, any triangle with three equal angles has three equal sides. 3. If a triangle has two equal angles, the sides opposite the two equal angles are equal in length, forming an isosceles triangle.

+ =

x y

180