<1 is supplemntary to <2. if m<1=4x-3 and m<2=3x+8, find the value of x

If \(\angle 1\) is supplementary to \(\angle 2\), then the sum of their measures is \(180^\circ\). This means:

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

Given:
\[
m\angle 1 = 4x - 3
\]
\[
m\angle 2 = 3x + 8
\]

We can set up the equation:

\[
(4x - 3) + (3x + 8) = 180
\]

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

\[
4x - 3 + 3x + 8 = 180
\]
\[
7x + 5 = 180
\]
\[
7x = 180 - 5
\]
\[
7x = 175
\]
\[
x = \frac{175}{7}
\]
\[
x = 25
\]

Thus, the value of \(x\) is \(25\).

---

Do you want details or have any questions about the solution? Here are 5 related questions to further your understanding:

1. How can we check if angles are supplementary in general?
2. What happens if two angles are complementary instead of supplementary?
3. How would the solution change if we were given angles in radians instead of degrees?
4. How can we apply this concept to real-world situations, such as design or architecture?
5. What are other types of angle relationships, and how do they differ from supplementary angles?

**Tip:** Always double-check the sum of supplementary angles; it should be exactly \(180^\circ\).

<1 is supplementary to <2. if m<1=4x-3 and m<2=3x+8, find the value of x

Learn how to solve the equation when two angles are supplementary. This problem involves the equation m<1 = 4x - 3 and m<2 = 3x + 8, where the sum of these angles equals 180°. A detailed step-by-step solution is provided, covering key concepts in algebra and geometry, suitable for students in Grades 8-10.

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