In the diagram above, the two lines marked with arrows are parallel. You are given the angle of 56^{o} and of 115^{o}. Find the angle x.

The angle $\displaystyle \alpha$ is the same as the 56^{o} angle, since the two lines marked with arrows are parallel and the line that crosses them must cross parallel lines at the same angle.

The angle Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle \displaystyle \beta}
is 180^{o}-115^{o} since it and the 115^{o} angle add up to a straight line. So it is 65^{o}.

We can now redraw the diagram with the angles as follows:

We have a triangle with angles x, 56^{o} and 65^{o}.

In the diagram above two angles are marked as 75^{o} and one as 101^{o}. Find the angle c.

There is an isosceles triangle with angles 75^{o}, 75^{o} and an unknown angle b. So

b+75^{o}+75^{o}=180^{o}.

b+150^{o}=180^{o}.

b=30^{o}.

$\displaystyle \angle BAC=101^{\circ }$

The angle 'c' is an angle in triangle Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \displaystyle \Delta ABC}
. The other two angles are 30^{o} and 101^{o}.