Problem-Solving Application

[annad95]

A billiard ball bounces off the sides of a rectangular billiards tables in such a way that angle 1 is congruent to angle 3, angle 4 is congruent to angle 6, and angle 3 and angle 4 are complementary. If m angle 1= 26.5 degrees, find m angle 3, m angle 4, and m angle 5.

 

[mmm4444bot]

What have you thought about so far, in this exercise?

 

[annad95]

angle 3= 26.5 degrees
angle 4= 26.5 degrees
angle 5= 13.25 degrees

 

[Mrspi]

angle 3= 26.5 degrees
angle 4= 26.5 degrees
angle 5= 13.25 degrees

Since it is given that <1 is congruent to <3, and that m<1 = 26.5 degrees, then you are correct in saying that m<3 = 26.5 degrees.

Did you notice that the problem states that <3 and <4 are complementary? What does that tell you? If <3 and <4 are complementary, can both of them have 26.5 degrees for their measures?

I also think that you've got a diagram which shows you where the various angles are located...and probably that will determine the measures of some of them. Since there is nothing mentioned in the problem about m<5, I think you're going to have to look for additional information in the diagram.

 

[soroban]

Hello, annad95!

A labeled diagram would have helped somewhat . . .

\(\displaystyle \text{A billiard ball bounces off the sides of a rectangular}\) \(\displaystyle \text{billiards tables in such a way that:}\)
. . \(\displaystyle \angle 1 = \angle 3,\;\angle 4 = \angle 6,\;\angle 3\text{ and }\angle 4\text{ are complementary.}\)

\(\displaystyle \text{If }\angle 1 = 26.5^o,\,\text{ find }\angle3,\;\angle 4,\,\text{ and }\,\angle 5.\)

I would guess that the situation looks like this:

      * - - - - - - - - - - - - - - *
      |                             |
      |                             |
      |                 *           |
      |                    *        |
      |                       *   6 |
      |                          *  |
      |     *                    5  *
      |        *                 *  |
      |           *     2     *   4 |
      |            1 *     * 3      |
      * - - - - - - - - * - - - - - *

We are told that \(\displaystyle \angle 1 = 26.5^o\), then \(\displaystyle \angle 3 = 26.5^o\)
Hence:. \(\displaystyle \angle 2 \:=\:180^o - 26.5^o - 26.5^o \:=\:127^o\)

Since \(\displaystyle \angle 3\) and \(\displaystyle \angle 4\) are complementary:. \(\displaystyle \angle 4 \:=\:90^o - 26.5^o \:=\:63.5^o\)
. . Then \(\displaystyle \angle 6 \:=\:63.5^o\)
Hence: .\(\displaystyle \angle 5 \:=\:180^o - 63.5^o - 63.5^o \:=\:53^o\)