Math, asked by deepajayadeep80, 7 months ago

triangle abc is an isoscles with ab =ac and side ac is produced to E if cd//ba find the value of x

Answers

Answered by hannu15102006
0

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\°

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