Math Problem Statement

Find the measure of the missing angles (x and y) based on a diagram with an angle of 38 degrees and a right angle.

Solution

The diagram you uploaded shows several angles formed by intersecting lines. We are tasked with finding the missing angles xx and yy.

Step-by-step solution:

  1. Identify known angles and relationships:

    • The diagram shows a 90° angle in the lower-right quadrant, which splits the vertical and horizontal lines.
    • The angle labeled 38° shares a straight line with angle xx, meaning these two angles are supplementary. So, x+38=180x + 38^\circ = 180^\circ.
  2. Find angle xx: Using the supplementary angle relationship: x=18038=142x = 180^\circ - 38^\circ = 142^\circ

  3. Find angle yy: The sum of the angles around the point where yy and the 90° angle meet must equal 180° because they form a straight line. y+90=180y + 90^\circ = 180^\circ Solving for yy: y=18090=90y = 180^\circ - 90^\circ = 90^\circ

Final Answer:

  • x=142x = 142^\circ
  • y=90y = 90^\circ

Would you like further clarification on these steps or more detailed explanations?

Here are 5 related questions for practice:

  1. If an angle is complementary to yy, what is its measure?
  2. What would the measure of xx be if the angle adjacent to it was 40° instead of 38°?
  3. What are supplementary angles, and why are xx and 38° supplementary?
  4. If the angle xx was bisected, what would each smaller angle measure?
  5. Can a right angle ever be supplementary? Explain why or why not.

Tip: Remember that supplementary angles always add up to 180°, while complementary angles sum to 90°.

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Math Problem Analysis

Mathematical Concepts

Geometry
Supplementary Angles
Right Angles

Formulas

x + 38° = 180°
y + 90° = 180°

Theorems

Supplementary Angles Theorem
Right Angle Theorem

Suitable Grade Level

Grades 6-8