1. **Problem:** Find the measure of angle A in triangle ABC where angles are given as $4x + 5$, $5x$, and $6x + 10$. 2. **Formula:** The sum of interior angles in a triangle is always $180^\circ$. 3. **Set up the equation:** $$ (4x + 5) + 5x + (6x + 10) = 180 $$ 4. **Simplify:** $$ 4x + 5 + 5x + 6x + 10 = 180 $$ $$ (4x + 5x + 6x) + (5 + 10) = 180 $$ $$ 15x + 15 = 180 $$ 5. **Isolate $x$:** $$ 15x + 15 = 180 $$ $$ 15x = 180 - 15 $$ $$ 15x = 165 $$ $$ x = \frac{165}{15} $$ $$ x = 11 $$ 6. **Calculate angle A:** $$ 4x + 5 = 4(11) + 5 = 44 + 5 = 49^\circ $$ 7. **Answer:** The measure of angle A is $49^\circ$, which corresponds to option C. --- **Note:** The second question is not solved as per instructions to solve only the first problem.