Explain how you can use a straightedge and a compass to construct an angle that is both congruent and adjacent to a given angle.

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Explain how you can use a straightedge and a compass to construct an angle that is both congruent and adjacent to a given angle.

Geometry
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Start with a given angle. |dw:1441049395859:dw|
Open the compass and center it at the vertex and draw an arc on each ray of the angle and an extra arc for the other ray we need for the adjacent congruent angle. |dw:1441049537826:dw|
Now open the compass from the arc one one ray to the arc on the other ray. That is open it from points A to B below. |dw:1441049636659:dw|

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Other answers:

Ok
Using opening AB, center the compass at B, and draw an arc that intersects the third arc we drew before.
|dw:1441049700977:dw|
Connect the vertex of the original angle with point D. You have now a congruent adjacent angle to the original angle. |dw:1441049765527:dw|
Oh ok, thank you !!
You're welcome. This construction works because of congruent triangles using SSS and CPCTC.
Uh, Math Student 55 has answered for you. Please remember! Great answer by the way Math Student 55. You have a lot of points.

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