Find the value of x  the angle b is equal to 45 and a equals to 80 c is equal to x exterior angle is 100

We are given the following information:

- Angle \( b = 45^\circ \)
- Angle \( a = 80^\circ \)
- Angle \( c = x \) (interior angle)
- The exterior angle at vertex \( c \) is \( 100^\circ \).

### Step-by-step solution:

1. **Exterior angle theorem**: 
   The exterior angle of a triangle is equal to the sum of the two opposite interior angles. So, for the exterior angle at \( c \), we have:
   \[
   100^\circ = a + b
   \]
   Substituting the values of \( a \) and \( b \):
   \[
   100^\circ = 80^\circ + 45^\circ
   \]
   \[
   100^\circ = 125^\circ
   \]
   But this is not true, indicating a contradiction in the given problem.

Could you clarify any missing information or any possible errors in the values provided? This will help solve the problem more accurately.

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Here are five related questions that expand upon the concept of angles and triangles:

1. What is the sum of interior angles in any triangle?
2. How do you calculate the third angle in a triangle if two angles are known?
3. Can an exterior angle ever be smaller than either of the two opposite interior angles?
4. What is the difference between an acute triangle and an obtuse triangle?
5. How do supplementary angles relate to an exterior angle?

**Tip:** Always double-check the sum of the angles in any triangle to ensure consistency, as they should always add up to 180°.

Find the value of x. The angle b is equal to 45°, a equals 80°, and c is equal to x (interior angle). The exterior angle is 100°.

Solve the problem of finding the value of x in a triangle where angle a is 80°, angle b is 45°, and the exterior angle at vertex c is 100°. This solution uses the Exterior Angle Theorem and is suitable for students in Grades 7-10.

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