Identifying Unknown Angles Worksheets | Geometry - Free Printable

To solve the problem of identifying the unknown angles in the given worksheet, we need to use basic geometric principles, such as the properties of straight lines, perpendicular lines, and supplementary angles. Let's go through each problem step by step.

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Problem 1:

- Given: A perpendicular line forming a right angle (90°).
- Unknown Angle: \( \angle xoz \)

Since \( \angle xoz \) is part of a right angle:
\[
\angle xoz = 90^\circ
\]

Answer: \( \angle xoz = 90^\circ \)

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Problem 2:

- Given: A straight line with one angle marked as \( 105^\circ \).
- Unknown Angle: \( \angle roq \)

Since \( \angle roq \) and \( 105^\circ \) are supplementary angles (they form a straight line):
\[
\angle roq + 105^\circ = 180^\circ
\]
\[
\angle roq = 180^\circ - 105^\circ = 75^\circ
\]

Answer: \( \angle roq = 75^\circ \)

---

Problem 3:

- Given: A straight line with one angle marked as \( 60^\circ \).
- Unknown Angle: \( \angle acd \)

Since \( \angle acd \) and \( 60^\circ \) are supplementary angles (they form a straight line):
\[
\angle acd + 60^\circ = 180^\circ
\]
\[
\angle acd = 180^\circ - 60^\circ = 120^\circ
\]

Answer: \( \angle acd = 120^\circ \)

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Problem 4:

- Given: A straight line with one angle marked as \( 30^\circ \).
- Unknown Angle: \( \angle acd \)

Since \( \angle acd \) and \( 30^\circ \) are supplementary angles (they form a straight line):
\[
\angle acd + 30^\circ = 180^\circ
\]
\[
\angle acd = 180^\circ - 30^\circ = 150^\circ
\]

Answer: \( \angle acd = 150^\circ \)

---

Problem 5:

- Given: A straight line with one angle marked as \( 135^\circ \).
- Unknown Angle: \( \angle xqp \)

Since \( \angle xqp \) and \( 135^\circ \) are supplementary angles (they form a straight line):
\[
\angle xqp + 135^\circ = 180^\circ
\]
\[
\angle xqp = 180^\circ - 135^\circ = 45^\circ
\]

Answer: \( \angle xqp = 45^\circ \)

---

Problem 6:

- Given: A straight line with one angle marked as \( 120^\circ \).
- Unknown Angle: \( \angle pts \)

Since \( \angle pts \) and \( 120^\circ \) are supplementary angles (they form a straight line):
\[
\angle pts + 120^\circ = 180^\circ
\]
\[
\angle pts = 180^\circ - 120^\circ = 60^\circ
\]

Answer: \( \angle pts = 60^\circ \)

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Problem 7:

- Given: A straight line with one angle marked as \( 15^\circ \).
- Unknown Angle: \( \angle xyb \)

Since \( \angle xyb \) and \( 15^\circ \) are supplementary angles (they form a straight line):
\[
\angle xyb + 15^\circ = 180^\circ
\]
\[
\angle xyb = 180^\circ - 15^\circ = 165^\circ
\]

Answer: \( \angle xyb = 165^\circ \)

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Problem 8:

- Given: A straight line with one angle marked as \( 100^\circ \).
- Unknown Angle: \( \angle soq \)

Since \( \angle soq \) and \( 100^\circ \) are supplementary angles (they form a straight line):
\[
\angle soq + 100^\circ = 180^\circ
\]
\[
\angle soq = 180^\circ - 100^\circ = 80^\circ
\]

Answer: \( \angle soq = 80^\circ \)

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Final Answers:

1. \( \angle xoz = 90^\circ \)
2. \( \angle roq = 75^\circ \)
3. \( \angle acd = 120^\circ \)
4. \( \angle acd = 150^\circ \)
5. \( \angle xqp = 45^\circ \)
6. \( \angle pts = 60^\circ \)
7. \( \angle xyb = 165^\circ \)
8. \( \angle soq = 80^\circ \)

\boxed{
\begin{aligned}
1. & \ 90^\circ \\
2. & \ 75^\circ \\
3. & \ 120^\circ \\
4. & \ 150^\circ \\
5. & \ 45^\circ \\
6. & \ 60^\circ \\
7. & \ 165^\circ \\
8. & \ 80^\circ
\end{aligned}
}