Skill: Find unknown angles around a point

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Angles meeting at a single point make a complete turn, so their measures sum to $360^\circ$ , regardless of their apparent size or orientation. The learner determines an unknown angle by interpreting the diagram as parts of a full turn and using addition or subtraction, including several known angles; the focus is on numerical angle measures rather than formal geometric proofs or generalized algebraic angle relationships.

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Detailed Explanation: Find unknown angles around a point

Angles that meet at one point make a complete turn. A complete turn is $360^\circ$ , so all the angles around the point add to $360^\circ$ .

Example: Around a point, three angles are $85^\circ$ , $120^\circ$ , and $70^\circ$ . Find the unknown angle $x$ .

Add the known angles:

85^\circ+120^\circ+70^\circ=275^\circ

Subtract this total from the full turn:

x=360^\circ-275^\circ

Calculate:

x=85^\circ

So, the unknown angle is $85^\circ$ .

Always check that all the angles add to $360^\circ$ :

85^\circ+120^\circ+70^\circ+85^\circ=360^\circ

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Geometry Polygon Exterior Angles - Polygon and Image to Missing Angle

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