Question

In the following diagrams, fins the value of $x$:

Answer 1

In following diagram given that $AB=AC$
That is $\angle B=\angle ACB$ ( angles opposite to equal sides in a triangle are equal )
Now, $\angle A+\angle B+\angle ACB={180}^o$
( sum of all angles in a triangle is ${180}^o$)
$50+\angle B+\angle B={180}^o$
$(\angle A={50}^o$ ( given ) $\angle B=\angle ACB)$
${50}^o+2\angle B={180}^o(2\angle B={180}^o-{50}^o$
$2\angle B={130}^o(\angle B=130/2={65}^o$
$\angle ACB={65}^o$
Also $\angle ACB+x^o={180}^o$ (Linear pair)
${65}^o+x^o={180}^o(x^o={180}^o-{65}^o$
$x^o={115}^o$
Hence, value of $x=115$