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Apply the triangle angle-sum relationship

The interior angles of every triangle have a sum of 180∘180^\circ, regardless of the triangle’s size, orientation, or classification, so a missing angle can be determined by subtracting known measures or solving an equation involving angle expressions. This understanding includes interpreting diagrams and numerical or algebraic angle measures, but not trigonometric applications or formal proof beyond using the angle-sum relationship.

Detailed Explanation: Apply the triangle angle-sum relationship

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

Angle 1+Angle 2+Angle 3=180∘\text{Angle 1}+\text{Angle 2}+\text{Angle 3}=180^\circ

To find a missing angle, add the known angles and subtract that sum from 180∘180^\circ.

Example: A triangle has angles measuring 52∘52^\circ, 67∘67^\circ, and x∘x^\circ. Find xx.

  1. Write the angle-sum equation:

52+67+x=180 52+67+x=180

  1. Add the known angles:

119+x=180 119+x=180

  1. Subtract 119119 from both sides:

x=61 x=61

The missing angle is:

61∘\boxed{61^\circ}

Check: 52∘+67∘+61∘=180∘52^\circ+67^\circ+61^\circ=180^\circ, so the answer is correct.

Learn by doing: Apply the triangle angle-sum relationship

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    Missing Angle on the Triangle

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