Triangles

In the triangle $ABC$, $\alpha ={80}^{\circ }$ and $\gamma ={30}^{\circ }$ (see the picture). Determine the measure of the angle between the altitude to the side $AC$ and the altitude to the side $AB$.

Consider a triangle $ABC$ with sides of the lengths $3\mathrm{cm}$, $4\mathrm{cm}$ and $4\mathrm{cm}$. Identify the type of the triangle $ABC$.

Consider a triangle $ABC$ with sides of the lengths $4\mathrm{cm}$, $4\mathrm{cm}$ and $4\mathrm{cm}$. Identify the type of the triangle $ABC$.

Consider an isosceles triangle $ABC$ with sides $AC$ and $BC$ of equal length. The measure of the angle $BAC$ is ${40}^{\circ }$. $X$ is the point of intersection between the line $AB$ and the line through the vertex $C$ perpendicular to it. Find the measure of the angle $BCX$.