#2**+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.

Gadfly Nov 16, 2019

#2**+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**+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!!)

hectictar Nov 16, 2019