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We are given two supplementary angles \( \angle 1 \) and \( \angle 2 \), with the expressions for their measures:

\[
m\angle 1 = 7x - 42 \quad \text{and} \quad m\angle 2 = 3x + 62.
\]

Since supplementary angles sum up to \(180^\circ\), we can set up the following equation:

\[
(7x - 42) + (3x + 62) = 180.
\]

Now let's solve this step by step.

### Step 1: Combine like terms
\[
7x - 42 + 3x + 62 = 180 \quad \Rightarrow \quad 10x + 20 = 180.
\]

### Step 2: Subtract 20 from both sides
\[
10x = 160.
\]

### Step 3: Divide by 10
\[
x = 16.
\]

### Step 4: Find the measures of \( \angle 1 \) and \( \angle 2 \)
Substitute \( x = 16 \) back into the expressions for \( \angle 1 \) and \( \angle 2 \):

\[
m\angle 1 = 7(16) - 42 = 112 - 42 = 70^\circ,
\]
\[
m\angle 2 = 3(16) + 62 = 48 + 62 = 110^\circ.
\]

Thus, \( \angle 1 = 70^\circ \) and \( \angle 2 = 110^\circ \).

The correct answer is:

\[
\boxed{\angle 1 = 70, \, \angle 2 = 110}.
\]

Would you like any further clarification on this?

Here are five related questions you can explore:
1. How do you define complementary angles?
2. What happens if two angles are congruent?
3. Can you have more than two angles that are supplementary?
4. What is the formula for finding the measure of an angle's complement?
5. How can we verify that the sum of two angles is \(180^\circ\) algebraically?

**Tip:** Always check if angles are supplementary, complementary, or congruent based on their relationships to ensure the correct approach in solving for unknowns!

∠1 and ∠2 are supplementary angles. m∠1 = 7x - 42, and m∠2 = 3x + 62. Find the measure of each angle.

Learn how to solve for two supplementary angles where m∠1 = 7x - 42 and m∠2 = 3x + 62. This problem uses algebraic methods to find the value of x and determine the measures of both angles. Suitable for students in Grades 7-9.

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