A triangle has angles 35° and 75°. Find the third.
Incorrect answer: 250°
The 180° total includes the interior angles only. If a diagram labels an exterior angle, first use its relationship with the adjacent interior angle or the two remote angles.
Using the wrong total for triangle angles
An ordinary plane triangle has interior angles totaling 180 degrees. Equal base angles share the remaining total.
The correction
70°
180 − 35 − 75 = 70.
- Identify the three interior angles; distinguish exterior labels from interior ones.
- Write a sum of 180° or an equivalent exterior-angle equation.
- Solve for the unknown and check all angle measures are positive.
Try the reasoning in another example
A triangle has angles x°, 2x°, and 3x°. Find all three.
- x + 2x + 3x = 180, so 6x = 180.
- x = 30; substitute into each expression.
Answer: 30°, 60°, 90°
Explain why each step preserves the quantity or relationship. If you can compute the answer but cannot explain the step, revisit the model before adding more questions.
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