In triangle $\mathrm{ABC}$, if angle $A$ measures $100°$ and angle $B$ measures $20°$, what is the measure of arc $\mathrm{BC}$ (the angle at vertex $C$)?

• A. $160°$
• B. $80°$
• C. $100°$
• D. $60°$

Answer: (D)

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: angle A is 100 degrees and angle B is 20 degrees.
3. Set up the equation for the sum of the angles: \(\text{angle A} + \text{angle B} + \text{angle C} = 180^\circ\).
4. Substitute the known values into the equation: \$100^\circ + 20^\circ + \text{angle C} = 180^\circ$.
5. Solve for angle C by isolating it: \(\text{angle C} = 180^\circ - 100^\circ - 20^\circ\).