https://file.aiquickdraw.com/mathbot/file/17273929214845bn60trb.jpg

Solve, explain fully to someone who knows nothing

To solve for all the angles in the given diagram, we need to use some key geometric principles such as **vertical angles**, **linear pairs**, and **corresponding angles** formed by parallel lines and a transversal.

### Step-by-Step Breakdown:

#### 1. Analyze the Known Angles:
- **Angle 44°** is given in the diagram at the top.
- **Angle 78°** is also given to the left of the point where multiple lines meet.
- **Angle 64°** is labeled near the bottom.

We'll use these known angles to find the other unknown angles: \( a \), \( b \), \( c \), \( d \), \( e \), and \( f \).

---

#### 2. Finding Angle \( f \) (Using a Linear Pair):
- Angles \( 78^\circ \) and \( f \) are on a straight line, meaning they form a linear pair. 
- The sum of angles on a straight line is always \( 180^\circ \).
  \[
  f = 180^\circ - 78^\circ = 102^\circ
  \]
Thus, \( f = 102^\circ \).

---

#### 3. Finding Angle \( e \) (Right Angle):
- Angle \( e \) is given as a right angle in the diagram. 
  \[
  e = 90^\circ
  \]
This is clearly indicated by the small square box inside angle \( e \).

---

#### 4. Finding Angle \( c \) (Using Vertical Angles):
- Angle \( c \) and the angle of \( 64^\circ \) directly opposite it form **vertical angles**, and vertical angles are always equal.
  \[
  c = 64^\circ
  \]

---

#### 5. Finding Angle \( d \) (Using a Linear Pair):
- Angles \( d \) and \( c \) are also on a straight line, forming a **linear pair**, so they must add up to \( 180^\circ \).
  \[
  d = 180^\circ - 64^\circ = 116^\circ
  \]
Thus, \( d = 116^\circ \).

---

#### 6. Finding Angle \( a \) (Using Corresponding Angles):
- Angle \( a \) corresponds to angle \( 44^\circ \) on parallel lines cut by a transversal. **Corresponding angles** are congruent, meaning they have the same measure.
  \[
  a = 44^\circ
  \]

---

#### 7. Finding Angle \( b \) (Using a Linear Pair):
- Angles \( a \) and \( b \) are on a straight line, forming a **linear pair**, so they must add up to \( 180^\circ \).
  \[
  b = 180^\circ - 44^\circ = 136^\circ
  \]
Thus, \( b = 136^\circ \).

---

### Final Answers:
- \( f = 102^\circ \)
- \( e = 90^\circ \)
- \( c = 64^\circ \)
- \( d = 116^\circ \)
- \( a = 44^\circ \)
- \( b = 136^\circ \)

Would you like any further details on these concepts?

---

### Related Questions:
1. What is the geometric rule for angles on a straight line?
2. How do you identify corresponding angles on parallel lines?
3. What is the definition of vertical angles?
4. How does the sum of angles in a triangle relate to these problems?
5. Can you solve for missing angles without knowing one of the angles?

### Tip:
In geometry, always look for relationships like linear pairs and vertical angles to easily find unknown angles!

Learn how to find the measures of angles in a geometric diagram involving parallel lines, transversals, and known angles. This problem explores key concepts like vertical angles, linear pairs, and corresponding angles. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation