SOLUTION: In the diagram of triangle ABC, side BC is extended to D [IMG]C:\Users\user\Pictures\p16a.gif[/IMG] If m<A= x^2-6x , m<B= 2x-3, and m<ACD= 9x+27, what is the value of x?

Question 733053: In the diagram of triangle ABC, side BC is extended to D
[IMG]C:\Users\user\Pictures\p16a.gif[/IMG]
If m
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
If
m< ,
m< , and
m< ,
what is the value of ?
recall:
The exterior angle theorem: the exterior angle of a triangle is equal to the sum of the two remote interior angles
so, m< =m< + m<
then you have

...factor...replace with

so, if ...=>.......this solution make equation true, but it could not work with angle measure because it cannot be negative
if ...=>......so, your solution is:

now find the measure of each angle:
m< ...=>..=>
m< ...=> ..=>
m< ...=>..=>

RELATED QUESTIONS
In the diagram below of triangle ABC, side BC is extended to D.... (answered by lynnlo)

Help please 1. Which of the following shows that ΔPQS ≅ ΔRQS, when... (answered by MathLover1)

Identify the sides of ΔMNO in order from shortest to longest.... (answered by MathLover1)

1. Identify the indicated sum. Image:... (answered by macston)

Given that A(0, 0), B(4, 0), C(0, 2), D(0, 0), E(12, 0), and F(0, 6), which of the... (answered by Fombitz,MathLover1)

in the accompanying diagram of ΔABC, AB is extended to E and D, exterior angle CBD... (answered by Edwin McCravy)

in triangle abc m∠a= x^2 m∠b= 11x+5 and m∠c= 13x-17 what is the longest (answered by Edwin McCravy)

1. in a triangle ABC angle=80 degree, if BD and CD are internal bisectors of angle B and... (answered by mananth)

A wall is 50 in. wide and 35 in. high. Will a mirror with a 62 in. diagonal fit in it?... (answered by MathLover1,gsmani_iyer)