91Ó°ÊÓ

Chapter 1 Basics of Geometry47. MATHEMATICAL CONNECTIONS In ?ABC, BX is in the interior of the angle, m?ABX is 12 more than 4 times m?CBX, and m?ABC= 92°.a. Draw a diagram to represent the situation.b. Write and solve an equation to ?nd m?ABXand m?CBX.

You are designing the living room of an apartment. Counting the floor, walls, and ceiling, you want the design to contain at least eight different planes. Draw a diagram of your design. Label each plane in your design.

THOUGHT PROVOKING The angle between the minute hand and the hour hand of a clock is 90°. What time is it? Justify your answer

Two coplanar intersecting lines will always intersect at one point. What is the greatest number of intersection points that exist if you draw four coplanar lines? Explain.

ABSTRACT REASONING Classify the angles that result from bisecting each type of angle. $$\begin{array}{ll}{\text { a. acute angle }} & {\text { b. right angle }} \\\ {\text { c. obtuse angle }} & {\text { d. straight angle }}\end{array}$$

You and your friend walk in opposite directions, forming opposite rays. You were originally on the corner of Apple Avenue and Cherry Court. a. Name two possibilities of the road and direction you and your friend may have traveled. b. Your friend claims he went north on Cherry Court, and you went east on Apple Avenue. Make an argument as to why you know this could not have happened.

CRITICAL THINKING The ray from the origin through (4, 0) forms one side of an angle. Use the numbers below as x- and y-coordinates to create each type of angle in a coordinate plane. $$\begin{array}{cccc}{-2} & {-1} & {0} & {1} & {2}\end{array}$$ $$\begin{array}{ll}{\text { a. acute angle }} & {\text { b. right angle }} \\\ {\text { c. obtuse angle }} & {\text { d. straight angle }}\end{array}$$

In Exercises \(51-54\) graph the inequality on a number line. Tell whether the graph is a segment, a ray or rays, a point, or a line. $$x \leq 3$$

The sum of the measures of two complementary angles is \(74^{\circ}\) greater than the difference of their measures. Find the measure of each angle. Explain how you found the angle measures.

MAKING AN ARGUMENT Your friend claims it is possible for a straight angle to consist of two obtuse angles. Is your friend correct? Explain your reasoning.