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To find the value of \( x \) in this triangle, let's use the fact that the sum of the angles in a triangle is always \( 180^\circ \).

The triangle has three angles:
1. \( 78^\circ \)
2. \( 42^\circ \)
3. \( x^\circ \)

Since the sum of all angles in a triangle is \( 180^\circ \), we can write the equation:
\[
78 + 42 + x = 180
\]

Adding \( 78 \) and \( 42 \):
\[
120 + x = 180
\]

Now, subtract \( 120 \) from both sides:
\[
x = 60
\]

So, the value of \( x \) is \( 60^\circ \).

Would you like a deeper explanation or have any questions?

Here are some related questions you might find interesting:
1. What is the rule for finding the missing angle in any triangle?
2. How can we determine if a triangle is acute, obtuse, or right?
3. What are the types of triangles based on their angles and sides?
4. Can the sum of two angles in a triangle ever exceed \(180^\circ\)?
5. How would the approach change if this was an exterior angle of a triangle?

**Tip:** Remember that the sum of interior angles in any triangle is always \(180^\circ\).

Find the value of x in a triangle with angles 78°, 42°, and x°.

Calculate the missing angle in a triangle where two angles are given as 78° and 42°. Learn about the Triangle Sum Theorem and understand how to use the angle sum formula to find the value of x. Suitable for students in Grades 6-8.

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