Question

$△ABC$ is an isosceles triangle, Find the value of $x$ .

• A. ${98}^o$
• B. $5^o$
• C. ${76}^o$
• D. ${52}^o$

Answer 1

The correct option is B $5^o$

Given, $△ABC$ is an Isosceles triangle.

We know, by isosceles triangle property, angles opposite to equal sides are equal.

Thus, $\angle BAC=\angle ACB={52}^o$.

Therefore, $y^o=\angle BAC={52}^o$.
We know, by angle sum property, the sum of the angles of a triangle is ${180}^{\circ }$ .

Then we have, ${52}^o+(14x+6{)}^o+{52}^o={180}^o$

$⟹$ ${104}^o+14x+6^o={180}^o$

$⟹$ ${110}^o+14x={180}^o$

$⟹$ $14x={180}^o-{110}^o$

$⟹$ $14x={170}^o-{110}^o={70}^o$

$⟹$$x=\frac{{70}^o}{14}=5^o$.

Therefore, option $B$ is correct.