Number 7

[aabbasi609]

HI guys i need some help oon number 7 on this thread. I need to do i in 7 steps but I'm doing it in 9. PLEASE HELPP

7.Given: Point K lies inside triangle ABC
Prove: measure of angle k is greater than measure of angle C

 

[Mrspi]

HI guys i need some help oon number 7 on this thread. I need to do i in 7 steps but I'm doing it in 9. PLEASE HELPP

7.Given: Point K lies inside triangle ABC
Prove: measure of angle k is greater than measure of angle C

Here's a thought.....

Extend segment BX to meet segment AC at a point we'll call D.

Now, we have a new triangle ADX, for which angle BXA is an exterior angle. The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle of the triangle. <ADX is an exterior angle, and so m<BXA > m<ADX.

Next, notice that <ADX is an exterior angle for triangle DCB. And so m<ADX is greater than the measure of either remote interior angle for triangle DCB. ONE of the remote interior angles is <C. Therefore, m<ADX > m<C.

Ok....if m<BXA > m<ADX, and m<ADX > m<C, what can you conclude, and why?