Math question!!

Test Preparation SAT Preparation
1

<p>The question is on pg 733 of BLUE SAT Book, number 15.</p>

<p>The question reads...</p>

<p>In the figure above, what is the sum, in terms of n, of the degrees measures of the four angles marked with arrows?</p>

<p>The image is here : <a href="http://img201.imageshack.us/img201/8923/mathproblem.png%5B/url%5D"&gt;http://img201.imageshack.us/img201/8923/mathproblem.png&lt;/a&gt;&lt;/p>

<p>The answer is = 2n</p>

<p>PLEASE PROVIDE FULL EXPLANATION OF THIS QUESTION AND STEP BY STEP HOW TO SOLVE IT :) ANY PLUG IN STRATEGIES ARE WELCOME :)</p>

2

<p>This is very simple. If you can post an image with all angles marked with with variable names. I will show you the details.</p>

3

<p>The picture is exactly as shown in the book. No variables were presented except for “n”. I have marked the four angles on the diagram but no degree/variable is provided. please help :)</p>

4

<p>Just mark all six angles in two triangles with arbitray names like a1 … a6 so that you know what I am talking about.</p>

5

<p>Each line is straight. This means that the unmarked angle inside each triangle has a degree measure of (180-n). Since a triangle has 180 degrees of all angle measures, make an equation for each triangle (both will be the same): 180=(180-n)+2x. Solve for n. n=2x. Do this for the other triangle. n=2x. This means that the four angles added together equal 2n. 2x times 2 (to yield all four angles) = 4x = 2n. I hope this helps!</p>

6

<p>Here is the new image with all the variables! Find the sum of a1+a2+a3+a4 :)</p>

<p><a href=“http://img139.imageshack.us/img139/8923/mathproblem.png[/url]”>http://img139.imageshack.us/img139/8923/mathproblem.png&lt;/a&gt;&lt;/p&gt;

7

<p>a1 + a2 + a5 = 180 (triange)
n + a5 = 180 (straight line)
=> a1 + a2 = n</p>

<p>a3 + a4 + a6 = 180
n + a6 = 180
=> a3 + a4 = n</p>

<p>Therefore: a1 + a2 + a3 + a4 = 2n</p>

8

<p>thanks dragonboy! :slight_smile: the only thing that is confusing me is
a1 + a2 = n and a3 + a4 = n how did you come up with those ?</p>

9

<p>If you understand these two Eqs:</p>

<p>a1 + a2 + a5 = 180 (triange) – Eq. 1
n + a5 = 180 (straight line) – Eq. 2</p>

<p>From Eq. 1: a1 + a2 = 180 - a5
From Eq. 2: n = 180 - a5
==> a1 + a2 = n = 180 - a5</p>

10

<p>gotcha! thanks</p>

11

<p>Actually, this (a1 + a2 = n) is a theorem:
“An exterior angle of a triangle is equal in measure to the sum of the two interior opposite angles.”</p>

<p>I am not sure it is covered in the american textbook.</p>