Practice worksheet for measuring angles and solving for unknown values in various geometric configurations.

I'll solve this worksheet step by step. The worksheet is titled "Angles, Angles, Everywhere!" and contains 8 problems asking to find angle measures or values of x.

Let me go through each problem one by one:

Problem 1: Find m∠ABC
Looking at the diagram, I can see that ∠ABC is composed of two adjacent angles: one measuring 30° and another measuring 45°. Since these angles are adjacent and form ∠ABC, I add them together:
m∠ABC = 30° + 45° = 75°

Problem 2: Find m∠ABC
In this diagram, ∠ABC appears to be a right angle (90°) with an additional 30° angle adjacent to it. So:
m∠ABC = 90° + 30° = 120°

Problem 3: Find m∠ABC
Here, ∠ABC is composed of three adjacent angles: 20°, 30°, and 40°. Adding them together:
m∠ABC = 20° + 30° + 40° = 90°

Problem 4: Find m∠ABC
This diagram shows ∠ABC as a straight angle (180°) minus a 60° angle. So:
m∠ABC = 180° - 60° = 120°

Problem 5: Find x
This is a square with a diagonal. In a square, all angles are 90°, and the diagonal bisects the corner angles. So each half-angle is 45°.
x = 45°

Problem 6: Find x
This is a rectangle with a diagonal. The diagonal creates two triangles. The angle marked x is in a right triangle where one angle is 90° and another is 30°. Since the sum of angles in a triangle is 180°:
x = 180° - 90° - 30° = 60°

Problem 7: Find x
This is a circle with a central angle of 120°. The remaining angle around the center would be:
x = 360° - 120° = 240°

Problem 8: Find x
This is a circle with a central angle of 90°. The remaining angle around the center would be:
x = 360° - 90° = 270°

Wait, let me reconsider problems 7 and 8. Looking more carefully at the diagrams, I believe these are asking for the measure of the arc or the reflex angle. However, given the context of the worksheet, it's more likely they're asking for the supplementary angle or the other part of the circle.

Actually, looking at the diagrams again, I think I need to be more precise. Let me re-examine each problem.

For problems 7 and 8, if we're looking at the angle marked x, which appears to be the larger angle going around the circle, then my initial calculation was correct.

Let me summarize my final answers:

1. m∠ABC = 75°
2. m∠ABC = 120°
3. m∠ABC = 90°
4. m∠ABC = 120°
5. x = 45°
6. x = 60°
7. x = 240°
8. x = 270°