Given a right triangle where angle $A$ measures $39°$ and side $\mathrm{BC}$ is the hypotenuse, what is the measure of arc $\mathrm{BC}$ in degrees?

• A. $78°$
• B. $102°$
• C. $129°$
• D. $39°$

Answer: (A)

Verified step by step guidance

1. Identify the type of triangle given: it is a right triangle, so one angle measures 90°.
2. Recall that the sum of the interior angles in any triangle is 180°, so use the equation: \(\text{Angle A} + \text{Angle B} + 90^\circ = 180^\circ\).
3. Substitute the known value of angle A (39°) into the equation: \(39^\circ + \text{Angle B} + 90^\circ = 180^\circ\).
4. Solve for angle B by isolating it: \(\text{Angle B} = 180^\circ - 90^\circ - 39^\circ\).
5. Understand that the measure of arc BC corresponds to twice the measure of angle A (since arc BC is the arc opposite angle A in the circle formed by the triangle's hypotenuse as diameter), so calculate \(\text{Arc BC} = 2 \times 39^\circ\).