Question

what is the value of x?

x =

Explanation:

Step1: Identify the triangle type

Since two sides of the triangle are equal (marked with red ticks), it is an isosceles triangle. In an isosceles triangle, the base - angles are equal. So, the angle opposite to the equal sides are equal. Let the base - angles be $\angle B=\angle C$.

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is $180^{\circ}$. We know one angle $\angle A = 36^{\circ}$. Let $\angle B=\angle C=x$. Then, using the formula $\angle A+\angle B+\angle C = 180^{\circ}$, we substitute the values:
$$36^{\circ}+x + x=180^{\circ}$$

Step3: Solve the equation for $x$

Combine like terms: $36^{\circ}+2x=180^{\circ}$.
Subtract $36^{\circ}$ from both sides: $2x=180^{\circ}- 36^{\circ}=144^{\circ}$.
Divide both sides by 2: $x=\frac{144^{\circ}}{2}=72^{\circ}$.

Answer:

$72$