triangle abc is an isoscles with ab =ac and side ac is produced to E if cd//ba find the value of x
Answers
Answer:
Given:
Δ ABC is an isosceles triangle.
AB = AC
AB ║CD
\angle ABC = 52\°∠ABC=52\°
We need to find the value of x.
Solution:
Δ ABC is an isosceles triangle.
AB = AC
\angle ABC = \angle ACB = 52\°∠ABC=∠ACB=52\°
Now we know that;
"Sum of all angles of a triangle is 180°."
so we can say that;
\angle ABC + \angle ACB + \angle BAC =180∠ABC+∠ACB+∠BAC=180
Substituting the values we get;
52\°+52\°+∠BAC=180\°
104\°+∠BAC=180\°
∠BAC=180\°−104\°
∠BAC=76\°
Now Given:
AB ║CD
so we can say that;
\angle BAC = \angle ACD∠BAC=∠ACD ⇒(Alternate angles)
\angle BAC = \angle ACD= 76\°∠BAC=∠ACD=76\°
Now we can say that;
\angle ACD + \angle DCE = 180\°∠ACD+∠DCE=180\° ⇒(Supplementary angles)
Substituting the values we get;
\begin{gathered}76\°+x =180\°\\\\x = 180\° - 76\°\\\\x = 104\°\end{gathered}
76\°+x=180\°
x=180\°−76\°
x=104\°