Question 65517
<pre><font size = 5><b>m<font face = "symbol">Ð</font>1:m<font face = "symbol">Ð</font>2 = 1:5. Find m<font face = "symbol">Ð</font>2

You have to know the measure of the sum of m<font face = "symbol">Ð</font>1 + m<font face = "symbol">Ð</font>2.
Otherwise you can't do the problem.

Were you told that <font face = "symbol">Ð</font>1 and <font face = "symbol">Ð</font>2 are 
complementary angles? Like this?:


|  /
|1/
|/2
 ¯¯¯¯¯¯
If so, then m<font face = "symbol">Ð</font>1 + m<font face = "symbol">Ð</font>2 = 90°

Let m<2 = x.  Then m<font face = "symbol">Ð</font>1 + x = 90°
                       m<font face = "symbol">Ð</font>1 = 90°-x

m<font face = "symbol">Ð</font>1:m<font face = "symbol">Ð</font>2 = 1:5

(90°-x):x = 1:5

Product of the means = product of the extremes

1x = 5(90° - x) 

 x = 450° - 5x 

6x = 450°

 x = 75°    

So m<font face = "symbol">Ð</font>2 = 75° 

Or, were you told that <font face = "symbol">Ð</font>1 and <font face = "symbol">Ð</font>2 are 
supplementary angles? Like this?:


       \    
        \  
        1\2 
 ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
If so, then m<font face = "symbol">Ð</font>1 + m<font face = "symbol">Ð</font>2 = 180°

Let m<font face = "symbol">Ð</font>2 = x.  Then m<font face = "symbol">Ð</font>1 + x = 180°
                       m<font face = "symbol">Ð</font>1 = 180°-x

m<font face = "symbol">Ð</font>1:m<font face = "symbol">Ð</font>2 = 1:5

(180°-x):x = 1:5

Product of the means = product of the extremes

1x = 5(180 - x) 

 x = 900° - 5x 

6x = 900°

 x = 150°    

So m<font face = "symbol">Ð</font>2 = 150° 

Edwin</pre>