We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
63
3
avatar

Find the sum of the orange angles.  Give a complete explanation.

 

 Nov 16, 2019

Best Answer 

 #2
avatar+70 
+3

The sum of the measures of the interior angles of the quadrilateral in the middle is 180(4-2) =360. This makes the sum of the four angles inside the four triangles that are opposite to the quadrilateral's interior angles, the ones that are not orange,  also 360 degrees. The sum of the interior angles of the four triangles is 4(180)= 720. So the orange angles must add up to 720-360= 360 as well.

 Nov 16, 2019
 #1
avatar+2499 
0

Are parrelel lines given?

 Nov 16, 2019
 #2
avatar+70 
+3
Best Answer

The sum of the measures of the interior angles of the quadrilateral in the middle is 180(4-2) =360. This makes the sum of the four angles inside the four triangles that are opposite to the quadrilateral's interior angles, the ones that are not orange,  also 360 degrees. The sum of the interior angles of the four triangles is 4(180)= 720. So the orange angles must add up to 720-360= 360 as well.

Gadfly Nov 16, 2019
 #3
avatar+8829 
+2

Here is an image to maybe help see this:

 

 

sum of green angles   =   4 * 180° because the sum of interior angles in each triangle is 180°
   
sum of pink angles  =   360°  because the sum of interior angles in a quadrilateral is 360°
  (see this by drawing two triangles inside a quadrilateral.)
   

sum of purple angles  =  sum of pink angles 

because vertical angles are congruent.
   

sum of orange angles  =  sum of green angles - sum of purple angles

 

sum of orange angles  =  4 * 180° - 360°

 

sum of orange angles  =  360°

 

(I apologize if you are colorblind!!)

 Nov 16, 2019

5 Online Users

avatar