Final answer:
To find the measures of angles B and C in the triangle, solve for x using the equation that the sum of angles in a triangle is 180°, then substitute x back into the expressions given for B and C.
Step-by-step explanation:
The correct answer is option 'Determine the measure of angle B (7x + 19°), angle C (8x + 13°), and angle A (16°) in triangle ABC'. Given that the sum of the angles in a triangle is always 180°, we can set up the following equation to solve for x:
7x + 19° + 8x + 13° + 16° = 180°
Combining like terms gives us:
15x + 48° = 180°
Subtracting 48° from both sides:
15x = 132°
Dividing by 15:
x = 8.8°
Now, plug x back into the expressions for angle B and C:
Angle B = 7(8.8°) + 19°
Angle C = 8(8.8°) + 13°
Finally, calculate the two angles:
Angle B = 61.6° + 19° = 80.6°
Angle C = 70.4° + 13° = 83.4°.