Question

In the given figure AB = AC, BAD = 50 and AD = AE. find the value of x

Answer 1

`x=25^o`

Explanation:

Angle sum of a triangle:
`< A + < B+ < C=180^o\\`

Types of Triangles: Isosceles, Equilateral, Scalene

Given AB = AC are two sides of the big triangle, then ΔABC is Isosceles.

Isosceles triangles are defined to have two equal sides and two equal angles (opposite the congruent(equal) sides).

Also, since ABC is defined as a triangle, BC is a straight line, a.k.a., it is a
`180^o` angle. As the image shows, the line, AD creates a right angle on one side, therefore it creates a right angle(
`90^o`) on the other side.

Back to Isosceles Triangles, AD = AE means ΔADE is isosceles and <ADE = <AED

Using the Angle sum formula of a triangle, you can fill in <A, <B, and <C with the following:

<A=
`50^o`

<B=<C=y [This is because <ADE = <AED]

`50^o+2y=180^o\\2y=130^o\\y=65^o`

Now, this means that <ADE=
`65^o` and <ADC =
`90^o`

<x is better seen as <EDC

<EDC+<ADE=<ADC

Since we know <ADE is 65 and <ADC is 90, we can plug in these to the formula above.

`x+65^o=90^o\\x=25^o`