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The problem involves two angles, \(\angle 1\) and \(\angle 2\), with the following conditions:

- \( m \angle 1 = (4x)^\circ \)
- \( m \angle 2 = (x - 5)^\circ \)

### (a) Write an equation with the "=" sign in it:
Since the angles \(\angle 1\) and \(\angle 2\) are adjacent and form a straight line, they are supplementary. That means their measures add up to \(180^\circ\). The equation is:

\[
m \angle 1 + m \angle 2 = 180^\circ
\]

Substitute the given values for the angles:

\[
(4x) + (x - 5) = 180
\]

### (b) Find the degree measures of \(\angle 1\) and \(\angle 2\):
Let's first solve for \(x\) by simplifying the equation from part (a):

\[
4x + x - 5 = 180
\]

\[
5x - 5 = 180
\]

\[
5x = 185
\]

\[
x = 37
\]

Now, substitute \(x = 37\) back into the expressions for \(\angle 1\) and \(\angle 2\):

\[
m \angle 1 = 4(37) = 148^\circ
\]

\[
m \angle 2 = 37 - 5 = 32^\circ
\]

So, the measures are:

- \(m \angle 1 = 148^\circ\)
- \(m \angle 2 = 32^\circ\)

Would you like further details or have any questions?

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Here are five related questions for practice:
1. What are supplementary angles, and how are they used to form equations?
2. If \( m \angle 1 = (3x + 10)^\circ \) and \( m \angle 2 = (2x - 20)^\circ \), how would you solve for \(x\)?
3. How can you verify that two angles are supplementary?
4. If the sum of the angles is not \(180^\circ\), what could that indicate about the situation?
5. How can this technique be applied to angles that are not adjacent but still related geometrically?

**Tip:** Always check that the sum of the angles satisfies the given relationship (like \(180^\circ\) for supplementary angles) to confirm your solution.

In the figure, m∠1 = (4x)° and m∠2 = (x - 5)°. (a) Write an equation with the '=' sign in it. (b) Find the degree measures of m∠1 and m∠2.

Learn how to solve for x and find the degree measures of m∠1 and m∠2 when given the equations m∠1 = 4x° and m∠2 = (x-5)°. This problem involves key concepts in algebra and geometry, specifically the use of supplementary angles. Suitable for students in Grades 7-9.

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