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Find a missing angle in a triangle

The measures of the three interior angles of a triangle have a sum of 180°, so a missing angle can be found by subtracting the two known angle measures from 180° and representing the relationship with an equation or labeled diagram. This understanding distinguishes the triangle’s interior angles from surrounding angles and is limited to straightforward numerical cases, not formal proofs, exterior-angle theorems, or complex algebraic expressions.

Detailed Explanation: Find a missing angle in a triangle

The three interior angles inside 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. Check that all three angles add to (180∘)(180^\circ).

Example

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

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∘x^\circ = 180^\circ - 110^\circ

So,

x=70∘\boxed{x = 70^\circ}

Check:

65∘+45∘+70∘=180∘65^\circ + 45^\circ + 70^\circ = 180^\circ

Therefore, the missing interior angle is 70∘\boxed{70^\circ}.

Learn by doing: Find a missing angle in a triangle

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    Missing Angle on the Triangle

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