Given two supplementary angles n and 2n+3, find the value of the two angles

Given two supplementary angles, their sum is \(180^\circ\). Let's denote the two angles as \(n\) and \(2n + 3\). 

Since they are supplementary:

\[
n + (2n + 3) = 180
\]

Simplify and solve for \(n\):

\[
n + 2n + 3 = 180
\]

\[
3n + 3 = 180
\]

Subtract 3 from both sides:

\[
3n = 177
\]

Now, divide by 3:

\[
n = 59
\]

Now that we have \(n\), let's find the value of the other angle:

\[
2n + 3 = 2(59) + 3 = 118 + 3 = 121
\]

So, the two angles are \(59^\circ\) and \(121^\circ\).

Would you like more details or have any questions?

Here are 5 related questions:
1. What are complementary angles, and how do they differ from supplementary angles?
2. If one angle is \(x\) and the other is \(3x + 10\), how would you find the angles if they are supplementary?
3. How do you find the value of angles when given a linear pair of angles?
4. What happens if you subtract the smaller angle from the larger angle in a pair of supplementary angles?
5. Can two acute angles be supplementary?

**Tip:** Remember that the sum of supplementary angles is always \(180^\circ\), regardless of their individual measures.

Learn how to find the values of two supplementary angles, n and 2n + 3, with a detailed step-by-step solution. This problem covers concepts in geometry, specifically supplementary angles and their sum of 180 degrees. Suitable for students in Grades 7-9.

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