Finding Right Triangle Angles Given One Angle is 50 Degrees More Than the Smallest
Apply the geometry problem-solving strategy to find the angle measures of a right triangle when one angle is defined in relation to the smallest angle.
Problem: The measure of one angle of a right triangle is degrees more than the measure of the smallest angle. Find the measures of all three angles.
- Read the problem.
- Identify what you are looking for: the measures of all three angles.
- Name: Choose a variable to represent the smallest angle. Let be the measure of the smallest angle. The second angle is degrees more, so its measure is . The third angle is a right angle, measuring .
- Translate: Write the triangle angle sum property equation and substitute the known expressions:
- Solve the equation. Combine like terms: . Subtract from both sides: . Divide by : . Substitute to find the other angles: the second angle is , and the third angle is .
- Check the solutions: Does ? Yes, .
- Answer: The three angles measure , , and .
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