I need help with this problem and problems like this. I know that to solve this problem I have to find which angles are the same and etc, but how do I know that. How can I see that two angles are the same or if their sum is a certain angle ?
For example like this problem:
In the following figure,AB ̅and ̅̅̅̅CD are parallel. Evaluate the angle x in terms of angles y and z.
How do I approach this problem ? Can you give me some tips for these types of problems ? I would really appreciate it.
$\endgroup$ 42 Answers
$\begingroup$$x=z+y$
If you extend AB, BD and AC you will se that the angle outside of B is $y$.
Since AB and DC are parallel, the internal angle next to D and inside the triangle with $z$ is equal to $y$.
The angle next to $x$ and inside the triangle with $z$ is therefore $180-(z+y)$
$x$ is therefore $z+y$.
$\endgroup$ 1 $\begingroup$Label angle $CDB$ as $y$ and use the exterior angle theorem for triangles in Euclidean geometry.
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