Question 1163536

Each side of Traingle ABC is produced. AB extends till D, AC extends till F and BC extends till E. If AB=AC, BD=BE and AF=DF, find angle ABC.
<pre>Borrowing Tutor @GREENESTAMPS' Diagram
*[illustration ADC_1163536_4.png].
AB = AC, so ∡ABC = ∡ACB
BD = BE, so ∡BDE = ∡BED
AF = DF, so ∡ADF = ∡FAD

Let ∡BDE be x
∡s BDE and ADF are the same
Then ∡BDE, ∡BED, and ∡CAB are each, x, as well

Since an exterior angle of a triangle is equal to the sum of its interior opposite angles, we can say that: ∡ABC = x + x, or 2x
In addition, ∡ACB also = 2x (AB = AC)
From ΔABC, its 3 angles are: x, 2x, and 2x. so we get: x + 2x + 2x = 180
5x = 180
{{{matrix(1,5, x, "=", 180/5, "=", 36o)}}}

Therefore, <b>∡ABC</b> = 2x = 2(36) = {{{highlight_green(72^o)}}}</pre>