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Use the triangle angle sum

The three interior angles of every triangle have a sum of 180°, so a known pair of angle measures determines an unknown angle by subtracting their sum from 180°. This relationship applies regardless of a triangle’s appearance or classification and supports representing geometric situations with simple equations; more advanced results involving exterior angles, polygons, or formal proofs are not included.

Detailed Explanation: Use the triangle angle sum

The three interior angles of every triangle add up to 180∘180^\circ.

To find a missing angle:

  1. Add the two known angles.
  2. Subtract that sum from 180∘180^\circ.
  3. Include the degree symbol.

Example: A triangle has angles measuring 65∘65^\circ, 45∘45^\circ, and x∘x^\circ. Find xx.

First, write an equation using the triangle angle sum:

65∘+45∘+x∘=180∘65^\circ+45^\circ+x^\circ=180^\circ

Add the known angles:

110∘+x∘=180∘110^\circ+x^\circ=180^\circ

Subtract 110∘110^\circ from both sides:

x∘=180∘−110∘=70∘x^\circ=180^\circ-110^\circ=70^\circ

So, the missing angle is:

70∘\boxed{70^\circ}

Check: 65∘+45∘+70∘=180∘65^\circ+45^\circ+70^\circ=180^\circ, so the answer is correct.

Learn by doing: Use the triangle angle sum

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    Missing Angle on the Triangle

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