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.