In triangle ABC, m∠A = 37° and m∠B = 89°. What is m∠C?
Understand the Problem
The question is asking us to find the measure of angle C in triangle ABC given the measures of angles A and B. To solve this, we can use the property that the sum of the angles in a triangle equals 180 degrees.
Answer
$m \angle C = 54^\circ$
Answer for screen readers
$m \angle C = 54^\circ$
Steps to Solve
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Identify the known angles Given the measures of angles A and B: $$ m \angle A = 37^\circ $$ $$ m \angle B = 89^\circ $$
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Use the triangle angle sum property The sum of the angles in a triangle is always 180 degrees. We can express this as: $$ m \angle A + m \angle B + m \angle C = 180^\circ $$
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Substitute the known values into the equation Replace $m \angle A$ and $m \angle B$ with their values: $$ 37^\circ + 89^\circ + m \angle C = 180^\circ $$
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Combine the angles A and B Calculate the sum of angles A and B: $$ 37^\circ + 89^\circ = 126^\circ $$
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Solve for the unknown angle C Subtract the sum of angles A and B from 180 degrees: $$ m \angle C = 180^\circ - 126^\circ $$
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Calculate the final measure of angle C Perform the subtraction: $$ m \angle C = 54^\circ $$
$m \angle C = 54^\circ$
More Information
In triangle ABC, the sum of the interior angles always equals 180 degrees. Using this principle, we can easily find the measure of the third angle once we know the other two.
Tips
- Forgetting that the sum of the triangle angles is 180 degrees.
- Miscalculating the sum of angles A and B, which can lead to an incorrect measure for angle C.
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