Calculate angles in geometric diagrams without measuring; solve for unknown angles using given angle values.

Problem: Calculate Angles — Show the Work

The task involves calculating various angles in geometric diagrams. Below, I will solve each problem step by step and explain the reasoning.

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#### Problem 1:
- Diagram: A straight line with two angles labeled as \(20^\circ\) and \(\angle ABC\).
- Task: Find \(\angle ABC\).

Solution:
1. A straight line forms a total angle of \(180^\circ\).
2. The given angle is \(20^\circ\).
3. Therefore, \(\angle ABC = 180^\circ - 20^\circ = 160^\circ\).

Answer: \(\boxed{160^\circ}\)

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#### Problem 2:
- Diagram: Two intersecting lines forming vertical angles. One angle is labeled as \(95^\circ\), and the other is \(\angle KLC\).
- Task: Find \(\angle KLC\).

Solution:
1. Vertical angles are equal.
2. The given angle is \(95^\circ\).
3. Therefore, \(\angle KLC = 95^\circ\).

Answer: \(\boxed{95^\circ}\)

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#### Problem 3:
- Diagram: A triangle with one angle labeled as \(77^\circ\) and another angle labeled as \(\angle ADC\). The third angle is not explicitly labeled but is part of the triangle.
- Task: Find \(\angle ADC\).

Solution:
1. The sum of the interior angles in a triangle is \(180^\circ\).
2. Let the unlabeled angle be \(x\). Then:
\[
77^\circ + x + \angle ADC = 180^\circ
\]
3. Since the diagram does not provide the value of \(x\), we assume it is the remaining angle in the triangle. However, if no additional information is given, we cannot determine \(\angle ADC\) uniquely without more data.

Note: The problem seems incomplete or missing information. If additional details are provided, please clarify.

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#### Problem 4:
- Diagram: A triangle with one angle labeled as \(135^\circ\) and another angle labeled as \(\angle EDC\). The third angle is not explicitly labeled but is part of the triangle.
- Task: Find \(\angle EDC\).

Solution:
1. The sum of the interior angles in a triangle is \(180^\circ\).
2. Let the unlabeled angle be \(x\). Then:
\[
135^\circ + x + \angle EDC = 180^\circ
\]
3. Since the diagram does not provide the value of \(x\), we assume it is the remaining angle in the triangle. However, if no additional information is given, we cannot determine \(\angle EDC\) uniquely without more data.

Note: The problem seems incomplete or missing information. If additional details are provided, please clarify.

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#### Problem 5:
- Diagram: A quadrilateral with one angle labeled as \(120^\circ\) and another angle labeled as \(\angle FGH\). The other two angles are not labeled.
- Task: Find \(\angle FGH\).

Solution:
1. The sum of the interior angles in a quadrilateral is \(360^\circ\).
2. Let the other two angles be \(x\) and \(y\). Then:
\[
120^\circ + x + y + \angle FGH = 360^\circ
\]
3. Since the diagram does not provide the values of \(x\) and \(y\), we cannot determine \(\angle FGH\) uniquely without more data.

Note: The problem seems incomplete or missing information. If additional details are provided, please clarify.

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#### Problem 6:
- Diagram: A triangle with one angle labeled as \(135^\circ\) and another angle labeled as \(\angle HJK\). The third angle is not explicitly labeled but is part of the triangle.
- Task: Find \(\angle HJK\).

Solution:
1. The sum of the interior angles in a triangle is \(180^\circ\).
2. Let the unlabeled angle be \(x\). Then:
\[
135^\circ + x + \angle HJK = 180^\circ
\]
3. Since the diagram does not provide the value of \(x\), we assume it is the remaining angle in the triangle. However, if no additional information is given, we cannot determine \(\angle HJK\) uniquely without more data.

Note: The problem seems incomplete or missing information. If additional details are provided, please clarify.

---

#### Problem 7:
- Diagram: A triangle with one angle labeled as \(111^\circ\) and another angle labeled as \(\angle JKL\). The third angle is not explicitly labeled but is part of the triangle.
- Task: Find \(\angle JKL\).

Solution:
1. The sum of the interior angles in a triangle is \(180^\circ\).
2. Let the unlabeled angle be \(x\). Then:
\[
111^\circ + x + \angle JKL = 180^\circ
\]
3. Since the diagram does not provide the value of \(x\), we assume it is the remaining angle in the triangle. However, if no additional information is given, we cannot determine \(\angle JKL\) uniquely without more data.

Note: The problem seems incomplete or missing information. If additional details are provided, please clarify.

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#### Problem 8:
- Diagram: A triangle with one angle labeled as \(120^\circ\) and another angle labeled as \(\angle MKL\). The third angle is not explicitly labeled but is part of the triangle.
- Task: Find \(\angle MKL\).

Solution:
1. The sum of the interior angles in a triangle is \(180^\circ\).
2. Let the unlabeled angle be \(x\). Then:
\[
120^\circ + x + \angle MKL = 180^\circ
\]
3. Since the diagram does not provide the value of \(x\), we assume it is the remaining angle in the triangle. However, if no additional information is given, we cannot determine \(\angle MKL\) uniquely without more data.

Note: The problem seems incomplete or missing information. If additional details are provided, please clarify.

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Final Answers:

1. \(\boxed{160^\circ}\)
2. \(\boxed{95^\circ}\)
3. Incomplete (missing information)
4. Incomplete (missing information)
5. Incomplete (missing information)
6. Incomplete (missing information)
7. Incomplete (missing information)
8. Incomplete (missing information)

If you have additional details or clarifications for any of the problems, please provide them, and I can refine the solutions accordingly.