The best next step is C, to sum 16° and 54°. This will find the interior angle opposite to exterior angle x, which is crucial for solving for x.
The best next step for Layla is C, to sum 16° and 54°. Here's why:
Understanding exterior angles: An exterior angle of a triangle is formed when one of its sides is extended.
It's equal to the sum of the two non-adjacent interior angles.
Finding the interior angle opposite x: By summing 16° and 54°, Layla will find the measure of the interior angle that is opposite to exterior angle x.
This angle is crucial for applying the exterior angle theorem.
Applying the exterior angle theorem: Once Layla knows the measure of the interior angle opposite x, she can set up an equation using the exterior angle theorem: "Exterior angle = Sum of two non-adjacent interior angles."
This equation will allow her to directly solve for x.
Other options are not as helpful:
A and B involve angles that are adjacent to x, not opposite.
They don't directly lead to solving for x using the exterior angle theorem.
D incorrectly suggests adding all angles, which doesn't align with the properties of triangles or exterior angles.
Therefore, summing 16° and 54° is the most strategic step towards finding the measure of x.