Find the measure of each angle 3z and 2z in a 180 degree angle

To find the measures of the angles 3z and 2z, we know that they are supplementary angles, meaning their sum is \(180^\circ\).

Given:
- One angle is \(3z\)
- The other angle is \(2z\)
- The sum of both angles is \(180^\circ\).

We can set up the equation as:
\[
3z + 2z = 180^\circ
\]

Simplifying the left-hand side:
\[
5z = 180^\circ
\]

Now, solve for \(z\) by dividing both sides by 5:
\[
z = \frac{180^\circ}{5} = 36^\circ
\]

Now that we know \(z = 36^\circ\), we can find the measures of both angles:
- The first angle is \(3z = 3 \times 36^\circ = 108^\circ\)
- The second angle is \(2z = 2 \times 36^\circ = 72^\circ\)

Thus, the measures of the angles are:
- \(3z = 108^\circ\)
- \(2z = 72^\circ\)

Would you like more details on this process?

Here are some related questions:
1. What are supplementary angles?
2. How do you determine the relationship between angles in a triangle?
3. How do you find unknown variables in angle equations?
4. What is the difference between complementary and supplementary angles?
5. Can angles have negative measures in real-world applications?

**Tip:** Always check if the angles sum up correctly after solving, especially in geometric problems!

Find the measure of each angle 3z and 2z in a 180 degree angle.

Learn how to calculate the measures of two supplementary angles 3z and 2z in a 180-degree angle. This solution covers the Supplementary Angle Theorem, linear equations, and key algebraic concepts. Suitable for students in Grades 6-8.

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