https://file.aiquickdraw.com/mathbot/file/1729547573292dn62vlyw.jpg

To solve for the missing angles \( x \) and \( y \) in this diagram, let's break it down:

1. The given angle is 40° and is adjacent to the angle labeled \( x \). These two angles form a straight line, which means they are supplementary. Supplementary angles add up to 180°.
   \[
   x + 40^\circ = 180^\circ
   \]
   Solving for \( x \):
   \[
   x = 180^\circ - 40^\circ = 140^\circ
   \]

2. The angle \( y \) is part of a right angle (90°) at the bottom-left corner, and it is vertically opposite to the angle next to \( x \), which is also 40°. Vertically opposite angles are equal, so:
   \[
   y = 40^\circ
   \]

Thus, the missing angles are:
- \( x = 140^\circ \)
- \( y = 40^\circ \)

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the relationship between vertically opposite angles?
2. How do complementary and supplementary angles differ?
3. Why do angles on a straight line always sum to 180°?
4. Can angles in different orientations be compared for equality in all cases?
5. How would you solve for angles if the diagram included a triangle?

**Tip:** Vertically opposite angles are always congruent, no matter the configuration of the lines.

Find the measure of the missing angles x and y.

Solve for missing angles x and y in a diagram using the concepts of supplementary angles and vertically opposite angles. This step-by-step solution is suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation