Given a right triangle, what is the measure of angle $A$ if $m\angle A$ is the smallest angle and the other two angles are $90°$ and $71°$?

• A. $19°$
• B. $42°$
• C. $82°$
• D. $21°$

Answer: (A)

Verified step by step guidance

1. Recall that the sum of the interior angles in any triangle is always 180 degrees. This is a fundamental property of triangles.
2. Identify the given angles in the triangle: one angle is 90° (since it's a right triangle), and another angle is given as 71°.
3. Let the measure of angle A be denoted as \(\angle A\). Since the sum of all angles must be 180°, set up the equation: \(\angle A + 90^\circ + 71^\circ = 180^\circ\).
4. Simplify the equation by adding the known angles: \(90^\circ + 71^\circ = 161^\circ\), so the equation becomes \(\angle A + 161^\circ = 180^\circ\).
5. Solve for \(\angle A\) by subtracting 161° from both sides: \(\angle A = 180^\circ - 161^\circ\). This will give the measure of angle A.