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How should the equation be entered into the text box for it to be right

Let's break down the problem step by step:

You are given the following angles:
- \( m \angle ABG = 150^\circ \)
- \( m \angle ABE = 65^\circ \)

We need to determine \( m \angle EBG \).

### Solution:
1. \( \angle ABG \) is made up of two angles, \( \angle ABE \) and \( \angle EBG \), so:
   \[
   m \angle ABG = m \angle ABE + m \angle EBG
   \]
2. Substituting the known values:
   \[
   150^\circ = 65^\circ + m \angle EBG
   \]
3. Solve for \( m \angle EBG \):
   \[
   m \angle EBG = 150^\circ - 65^\circ = 85^\circ
   \]

### Final Answer:
The measure of \( \angle EBG \) is \( 85^\circ \).

You should enter into the text box:
\[
m \angle EBG = 85^\circ
\]

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Do you want further details or have any questions?  
Here are 5 related questions to expand your understanding:

1. What is the sum of the angles on a straight line?
2. How would you solve if a different angle was unknown?
3. What geometric properties are used to solve problems like this one?
4. How are adjacent angles related in geometry?
5. Can you think of another method to check your answer?

**Tip:** When solving angle problems, always check for supplementary and complementary relationships to ensure your calculations are correct.

Given m < ABG = 150 and m < ABE = 65, what is the m < EBG?

Learn how to calculate the measure of angle EBG given m < ABG = 150° and m < ABE = 65°. This solution demonstrates key concepts in geometry, such as angle addition and supplementary angles. Suitable for students in Grades 6-8.

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