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The problem involves a triangle where two of the angles are given: one is \(45^\circ\) and the other is \(y - 12^\circ\). We are asked to find the value of \(y\).

The **Triangle Angle Sum Theorem** tells us that the sum of the angles in any triangle is always \(180^\circ\). Let's denote the angles as follows:

1. First angle: \(45^\circ\)
2. Second angle: \(y - 12^\circ\)
3. Third angle: \(y + 3^\circ\)

Using the theorem:
\[
45^\circ + (y - 12^\circ) + (y + 3^\circ) = 180^\circ
\]

Now, let's solve this equation step by step:

\[
45 + (y - 12) + (y + 3) = 180
\]

Simplifying:
\[
45 + y - 12 + y + 3 = 180
\]
\[
2y + 36 = 180
\]

Subtract 36 from both sides:
\[
2y = 144
\]

Divide by 2:
\[
y = 72
\]

Thus, the value of \(y\) is \(72^\circ\).

Would you like further details on this solution? Let me know if you have any questions.

Here are 5 related questions:
1. What is the Triangle Angle Sum Theorem?
2. How do you solve for unknown angles in any triangle?
3. What is an exterior angle in a triangle, and how does it relate to interior angles?
4. Can a triangle have two angles greater than 90 degrees? Why or why not?
5. How do supplementary and complementary angles relate to triangle problems?

**Tip**: Always double-check your math when solving for unknown angles to ensure you properly apply the Triangle Angle Sum Theorem.

What is the value of y in the triangle where one angle is 45° and the other two angles are expressed as y - 12° and y + 3°?

In this problem, a triangle is given with one angle as 45° and two unknown angles expressed in terms of y. Learn how to find the value of y using the Triangle Angle Sum Theorem and algebraic methods. This problem involves solving linear equations and is ideal for students in Grades 8-10.

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