https://file.aiquickdraw.com/mathbot/file/1729547615948p1mk12fn.jpg

This problem involves angles around a point. The sum of all angles around a point is always 360°. We are given two of the angles: 46° and 103°, and we need to find the angles labeled \( d \), \( e \), and \( f \).

### Steps to Solve:
1. **Find \( f \)**:
   - \( f \) is vertically opposite to the angle 103°.
   - Vertically opposite angles are equal, so:
     \[
     f = 103^\circ
     \]

2. **Find \( d \)**:
   - \( d \) is vertically opposite to the angle 46°.
   - Vertically opposite angles are also equal, so:
     \[
     d = 46^\circ
     \]

3. **Find \( e \)**:
   - The sum of angles around the point is 360°.
   - We already know the values of three angles: 46°, 103°, and 103° (from \( f \)).
   - The remaining angle \( e \) can be found by subtracting the sum of the known angles from 360°:
     \[
     e = 360^\circ - (46^\circ + 103^\circ + 103^\circ) = 360^\circ - 252^\circ = 108^\circ
     \]

### Final Answers:
- \( d = 46^\circ \)
- \( e = 108^\circ \)
- \( f = 103^\circ \)

Let me know if you need more details or further clarifications!

Here are 5 related questions:
1. What is the sum of all angles at a point?
2. How do vertically opposite angles relate to each other?
3. Can the sum of angles on a straight line be used to solve this?
4. What is the complementary relationship between adjacent angles?
5. How can we check if our calculated angles are correct?

**Tip:** Vertically opposite angles are always equal, which simplifies many geometric problems!

Find the measure of the missing angles (d, e, f) based on the given angles 46° and 103°.

Learn how to find the missing angles (d, e, f) in a geometry problem with angles around a point. We use the sum of angles at a point (360°) and the property of vertically opposite angles to solve the problem step by step. 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