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The problem states that ∠1 and ∠2 are supplementary angles. Supplementary angles sum up to 180°. Therefore, we can set up the equation:

\[
m\angle1 + m\angle2 = 180^\circ
\]

We are given:
- \( m\angle1 = (4x + 9)^\circ \)
- \( m\angle2 = (3x - 4)^\circ \)

Substitute these expressions into the supplementary angle equation:

\[
(4x + 9) + (3x - 4) = 180
\]

Now let's solve for \(x\):

\[
4x + 9 + 3x - 4 = 180
\]
\[
7x + 5 = 180
\]
\[
7x = 175
\]
\[
x = 25
\]

Now that we have the value of \(x\), substitute \(x = 25\) into the expression for \(m\angle2\):

\[
m\angle2 = 3x - 4 = 3(25) - 4 = 75 - 4 = 71^\circ
\]

Thus, the measure of ∠2 is \(71^\circ\).

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. What is the measure of ∠1 using \(x = 25\)?
2. If ∠1 were given by a different expression, how would it affect the value of ∠2?
3. How do supplementary and complementary angles differ in terms of their sum?
4. Can you solve for both angles if the problem involved complementary angles instead?
5. What if one of the angles were expressed in terms of \(y\) instead of \(x\)?

**Tip:** Always ensure the total sum of supplementary angles is 180° to verify correctness!

∠1 and ∠2 are supplementary angles. If m∠1 = (4x + 9)° and m∠2 = (3x - 4)°, then find the measure of ∠2.

Learn how to solve for the measure of angle ∠2 when m∠1 = (4x + 9)° and m∠2 = (3x - 4)°, given that they are supplementary angles. This step-by-step solution covers key algebraic concepts and theorems suitable for students in Grades 8-10.

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