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To solve for the angle \( t^\circ \) in the given triangle, we'll use the property that the sum of the angles in a triangle is always \( 180^\circ \).

### Step 1: Identify the angles in the triangle.
- The given angles are \( 18^\circ \), \( t^\circ \), \( 27^\circ \), and \( 68^\circ \).

### Step 2: Find the unknown angle inside the smaller triangle.
- The small triangle includes angles \( 18^\circ \), \( t^\circ \), and an unknown angle, which we'll call \( x^\circ \).
- Since the sum of angles in a triangle is \( 180^\circ \):
  \[
  18^\circ + t^\circ + x^\circ = 180^\circ
  \]
  \[
  x^\circ = 180^\circ - 18^\circ - t^\circ = 162^\circ - t^\circ
  \]

### Step 3: Use the larger triangle.
- The larger triangle includes angles \( 27^\circ \), \( 68^\circ \), and the angle \( x^\circ \) we found earlier.
- Again, the sum of the angles in a triangle is \( 180^\circ \):
  \[
  27^\circ + 68^\circ + x^\circ = 180^\circ
  \]
  \[
  x^\circ = 180^\circ - 95^\circ = 85^\circ
  \]

### Step 4: Solve for \( t^\circ \).
- Now we set the equation for \( x^\circ \) equal to the two expressions we've derived:
  \[
  162^\circ - t^\circ = 85^\circ
  \]
  \[
  t^\circ = 162^\circ - 85^\circ = 77^\circ
  \]

Thus, the value of \( t^\circ \) is **77 degrees**.

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How do you verify the angle sum in a triangle?
2. What are some common properties of angles in triangles?
3. How can the exterior angle theorem be applied to this problem?
4. What are other methods to solve for unknown angles in a triangle?
5. Can the concept of supplementary angles be useful in triangle problems?
6. How does knowing one angle help find the others in a right triangle?
7. What would change if the triangle was an isosceles triangle?
8. What role does trigonometry play in solving such problems?

**Tip:** Always double-check that the sum of the calculated angles equals \( 180^\circ \) to ensure accuracy.

Learn how to find the measure of angle t in a triangle using the angle sum property. Step-by-step solution provided with detailed calculations for angles 18°, 27°, and 68°. Suitable for students in Grades 7-9 studying geometry.

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