Finding the Third Angle of a Triangle Given Two Angles
Apply the geometry problem-solving strategy to find an unknown angle when two angles of a triangle are given.
Problem: The measures of two angles of a triangle are and . Find the measure of the third angle.
- Read and draw: Sketch a triangle and label the known angles and ; label the unknown angle .
- Identify: The measure of the third angle.
- Label: Let = the measure of the unknown angle.
- Translate: Apply the triangle angle sum property: .
- Solve: Combine the known values: . Subtract 137 from both sides: .
- Check: Verify the sum: , which is true.
- Answer: The measure of the third angle is .
This example illustrates how the triangle angle sum property converts a geometry question into a simple one-step linear equation.
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