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# Based on the diagram X=_____? Briefly explain your reasoning?

Posted by t4trendesetter on March 23, 2013 at 7:38 PM via web and tagged with exterior angle of a triangle, geometry, math

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In geometry there are often several ways to solve and various reasons you can use.

The first and largest triangle has

a right angle = 90 degrees (given)

and a 50 degree angle (given)

`therefore` the remaining angle = 180 - (90+50)= 40 degrees (angles of a triangle always = 180)

There is an exterior angle adjacent to our 40 degree angle which therefore = 140 degrees( angles on a straight line = 180)

In the second triangle we have a right angle=90 degrees (given)

We have an angle named `2x`  ( as yet unknown)

and another unknown angle which = 180- 140=40 degrees (angles on a straight line). It is on the same line as the previously proven 140 degrees above)

`therefore 2x= 180-(90+40)`  (angles of a triangle =180 deg)

`therefore 2x=50 ` degrees

`therefore x= 50/2`

`= 25`

`therefore` x=25

Posted by durbanville on March 23, 2013 at 8:12 PM (Answer #1)