Math Problem Statement

Find the measure of the missing angles in a diagram with a 33° angle, a right angle, and two unknown angles x and y.

Solution

Let's analyze the image step by step to find the missing angles, xx and yy.

  1. Understanding the setup:

    • The diagram shows multiple lines intersecting at a point.
    • One of the given angles is 3333^\circ, and we are asked to find the angles xx and yy.
    • There is also a right angle 9090^\circ formed by two perpendicular lines, which will help in solving the angles.
  2. Applying the straight angle property:

    • A straight angle measures 180180^\circ, so the total of angles around a straight line must equal 180180^\circ.
    • The angle adjacent to xx, which includes the angle 3333^\circ, forms a straight line. Therefore, x+33=180x + 33^\circ = 180^\circ.

    x=18033=147x = 180^\circ - 33^\circ = 147^\circ

  3. Using the right angle to find yy:

    • We know there is a right angle where the line containing yy meets the horizontal line, so the total of the angles around this point must equal 9090^\circ. Since x=147x = 147^\circ, the remaining part forms a vertical line perpendicular to the horizontal line.

    The sum of angles around a point is 360360^\circ, so:

    90+33+y=18090^\circ + 33^\circ + y = 180^\circ

    Solving for yy:

    y=1809033=57y = 180^\circ - 90^\circ - 33^\circ = 57^\circ

Final Answers:

  • x=147x = 147^\circ
  • y=57y = 57^\circ

Would you like more details on the calculation or a breakdown of the concepts?

Here are five follow-up questions based on this problem:

  1. What is the sum of the angles around a point?
  2. How do you calculate the missing angle when you have a straight line?
  3. What is the measure of a right angle in degrees?
  4. Why is x+33x + 33^\circ equal to 180° in this context?
  5. Can you find the value of angle yy if angle xx were different?

Tip: When solving for angles in geometry, always look for straight lines (180°) and right angles (90°) to help determine unknown values.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Angle Relationships
Straight Angles
Right Angles

Formulas

x + 33° = 180° (Straight angle)
y + 90° + 33° = 180° (Angles around a point)

Theorems

The sum of angles around a straight line is 180°
The sum of angles around a point is 360°
Right angle = 90°

Suitable Grade Level

Grades 7-9