https://file.aiquickdraw.com/mathbot/file/17260769964167q6kk9r1.jpg

To help you solve the problem in the image, let's break it down:

### (a) Write an equation to find \( x \).

From the figure, we are given:
- \( m \angle 1 = (x - 15)^\circ \)
- \( m \angle 2 = (4x)^\circ \)

Since angles 1 and 2 are adjacent and form a straight line, they are supplementary, meaning the sum of their measures equals \( 180^\circ \). 

The equation is:
\[
(x - 15) + 4x = 180
\]

### (b) Find the degree measure of each angle.

1. First, solve for \( x \) from the equation in part (a):
   \[
   (x - 15) + 4x = 180
   \]
   Simplify and solve:
   \[
   5x - 15 = 180
   \]
   \[
   5x = 195
   \]
   \[
   x = 39
   \]

2. Now, find the measures of each angle:
   - \( m \angle 1 = (x - 15) = 39 - 15 = 24^\circ \)
   - \( m \angle 2 = 4x = 4 \times 39 = 156^\circ \)

Thus, the degree measures of the angles are:
- \( m \angle 1 = 24^\circ \)
- \( m \angle 2 = 156^\circ \)

Would you like a more detailed explanation on solving the equation, or do you have any other questions?

### Related Questions:
1. How do you know that two angles are supplementary?
2. What are complementary angles, and how are they different from supplementary angles?
3. If angle 1 was \( (2x + 10)^\circ \), how would you set up the equation?
4. How can we solve for an unknown angle in a triangle?
5. What are vertical angles, and how do their measures relate?

### Tip:
Always remember to check whether angles are supplementary or complementary based on the geometric figure, as this often provides a key clue for setting up your equations.

In the figure, m ∠ 1 = (x - 15)° and m ∠ 2 = (4x)°. Find the value of x and the degree measure of each angle.

Learn how to solve for x in a supplementary angles problem where m ∠ 1 = (x - 15)° and m ∠ 2 = 4x. This problem involves solving linear equations and applying the supplementary angles theorem. Suitable for students in Grades 6-8.

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