Geometrical Optics - Light ray angles on a spherical mirror

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upload_2018-11-20_20-41-22.png

I can't see how the textbook produces the following relationships between angles:
$$ \theta = \phi + \alpha \qquad (1)$$
$$ 2\theta = \alpha + \alpha ' \qquad (2)$$

My thinking is that the exterior angle theorem for triangles was used to create expression ##(1)##, but I am unsure as to how expression ##(2)## came about. Was the exterior angle theorem simply used twice to produce both equations?
 

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  • #2
DaveC426913
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(2) comes about by the exact same theorem as (1).

2θ,α,α′ is the identical setup as θ,α,ϕ - it just makes a stubbier triangle.

angles.png
 

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