Question

what is the value of u?
work it out
not feeling ready yet? these can help:
triangle angle - sum theorem (68)
classify triangles (100)

Explanation:

Step1: Determine the type of triangle

Since two sides of the triangle are marked as equal, it is an isosceles triangle. In an isosceles triangle, the base angles are equal. So, $\angle C=\angle A = u$.

Step2: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is $180^{\circ}$. So, $\angle A+\angle B+\angle C = 180^{\circ}$. Substituting $\angle A = u$, $\angle C = u$, and $\angle B=86^{\circ}$, we get the equation $u + 86^{\circ}+u=180^{\circ}$.

Step3: Simplify the equation

Combine like terms: $2u+86^{\circ}=180^{\circ}$. Then, subtract $86^{\circ}$ from both sides: $2u=180^{\circ}-86^{\circ}$. So, $2u = 94^{\circ}$.

Step4: Solve for $u$

Divide both sides of the equation $2u = 94^{\circ}$ by 2. We get $u=\frac{94^{\circ}}{2}$.

Answer:

$47$